A high order boundary element method was developed for the complex velocity potential problem. The method ensures not only the continuity of the potential at the nodes of each element but also the velocity. It can be ...A high order boundary element method was developed for the complex velocity potential problem. The method ensures not only the continuity of the potential at the nodes of each element but also the velocity. It can be applied to a variety of velocity potential problems. The present paper, however, focused on its application to the problem of water entry of a wedge with varying speed. The continuity of the velocity achieved herein is particularly important for this kind of nonlinear free surface flow problem, because when the time stepping method is used, the free surface is updated through the velocity obtained at each node and the accuracy of the velocity is therefore crucial. Calculation was made for a case when the distance S that the wedge has travelled and time t follow the relationship s=Dtα, where D and α are constants, which is found to lead to a self similar flow field when the effect due to gravity is ignored.展开更多
For any group G, denote byπe(G) the set of orders of elements in G. Given a finite group G, let h(πe (G)) be the number of isomorphism classes of finite groups with the same set πe(G) of element orders. A group G i...For any group G, denote byπe(G) the set of orders of elements in G. Given a finite group G, let h(πe (G)) be the number of isomorphism classes of finite groups with the same set πe(G) of element orders. A group G is called k-recognizable if h(πe(G)) = k <∞, otherwise G is called non-recognizable. Also a 1-recognizable group is called a recognizable (or characterizable) group. In this paper the authors show that the simple groups PSL(3,q), where 3 < q≡±2 (mod 5) and (6, (q-1)/2) = 1, are recognizable.展开更多
A higher order boundary element method(HOBEM)is presented for inviscid flow passing cylinders in bounded or unbounded domain.The traditional boundary integral equation is established with respect to the velocity poten...A higher order boundary element method(HOBEM)is presented for inviscid flow passing cylinders in bounded or unbounded domain.The traditional boundary integral equation is established with respect to the velocity potential and its normal derivative.In present work,a new integral equation is derived for the tangential velocity.The boundary is discretized into higher order elements to ensure the continuity of slope at the element nodes.The velocity potential is also expanded with higher order shape functions,in which the unknown coefficients involve the tangential velocity.The expansion then ensures the continuities of the velocity and the slope of the boundary at element nodes.Through extensive comparison of the results for the analytical solution of cylinders,it is shown that the present HOBEM is much more accurate than the conventional BEM.展开更多
In this paper, a new higher order Wilson element is presented, and the convergence is proved. Then the interpolation postprocessing technique is used to obtain the global superconvergence and posterior error estimate ...In this paper, a new higher order Wilson element is presented, and the convergence is proved. Then the interpolation postprocessing technique is used to obtain the global superconvergence and posterior error estimate of higher accuracy of this new element for the Sobolev type equations.展开更多
A new kind of material cast polyurethane elastomers (CPUE) is introduced to take the place of rubber on load bearing wheel for the first time. Based on load bearing wheel dimensions, material properties and operatin...A new kind of material cast polyurethane elastomers (CPUE) is introduced to take the place of rubber on load bearing wheel for the first time. Based on load bearing wheel dimensions, material properties and operating conditions, the structure of wheel flange is optimized by zero order finite element method. A detailed three dimensional finite element model of flange of load bearing wheel is developed and utilized to optimize structure of wheel flange. Its service life, which is affected by flange structure parameter, is analyzed by comparing the optimization results with those of prototype of wheel. The results of optimization are presented and the stress field of load bearing wheel in optimal dimension obtained by using finite element analysis method is demonstrated. The finite element analysis and optimization results show that the CPUE load bearing wheel is feasible and suitable for the tracked vehicle and has a guiding value in practice of the weighting design of the whole tracked vehicle.展开更多
This paper aims at treating a study on the order of every element for addition and multiplication composition in the higher order of groups for different algebraic structures as groups;order of a group and order of el...This paper aims at treating a study on the order of every element for addition and multiplication composition in the higher order of groups for different algebraic structures as groups;order of a group and order of element of a group in real numbers. Here we discuss the higher order of groups in different types of order which will give us practical knowledge to see the applications of the addition and multiplication composition. If G is a finite group, n is a positive integer and a ⋴G, then the order of the products na. When G is a finite group, every element must have finite order. However, the converse is false: there are infinite groups where each element has finite order. For example, in the group of all roots of unity in C<sup>×</sup> each element has finite order. Finally, we find out the order of every element of a group in different types of higher order of group.展开更多
The finite element method （FEM） is employed to analyze the resonant oscillations of the liquid confined within multiple or an array of floating bodies with fully nonlinear boundary conditions on the free surface and...The finite element method （FEM） is employed to analyze the resonant oscillations of the liquid confined within multiple or an array of floating bodies with fully nonlinear boundary conditions on the free surface and the body surface in two dimensions. The velocity potentials at each time step are obtained through the FEM with 8-node quadratic shape functions. The finite element linear system is solved by the conjugate gradient （CG） method with a symmetric successive overelaxlation （SSOR） preconditioner. The waves at the open boundary are absorbed by the combination of the damping zone method and the Sommerfeld-Orlanski equation. Numerical examples are given by an array of floating wedge- shaped cylinders and rectangular cylinders. Results are provided for heave motions including wave elevations, profiles and hydrodynamic forces. Comparisons are made in several cases with the results obtained from the second order solution in the time domain. It is found that the wave amplitude in the middle region of the array is larger than those in other places, and the hydrodynamic force on a cylinder increases with the cylinder closing to the middle of the array.展开更多
A fully nonlinear numerical wave tank (NWT) has been simulated by use of a three-dimensional higher order boundary element method (HOBEM) in the time domain. Within the frame of potential flow and the adoption of simp...A fully nonlinear numerical wave tank (NWT) has been simulated by use of a three-dimensional higher order boundary element method (HOBEM) in the time domain. Within the frame of potential flow and the adoption of simply Rankine source, the resulting boundary integral equation is repeatedly solved at each time step and the fully nonlinear free surface boundary conditions are integrated with time to update its position and boundary values. A smooth technique is also adopted in order to eliminate the possible saw-tooth numerical instabilities. The incident wave at the uptank is given as theoretical wave in this paper. The outgoing waves are absorbed inside a damping zone by spatially varying artificial damping on the free surface at the wave tank end. The numerical results show that the NWT developed by these approaches has a high accuracy and good numerical stability.展开更多
In this paper, we characterize some simple Ka-groups only by using the group order and largest element orders, where a simple K4-group is a simple group of order containing exactly four distinct primes.
The present study concerns the modelization and numerical simulation for the heat and flow exchange characteristics in a novel configuration saturated with a nonNewtonian Ag-MgO hybrid nanofluid.The wavy shaped enclos...The present study concerns the modelization and numerical simulation for the heat and flow exchange characteristics in a novel configuration saturated with a nonNewtonian Ag-MgO hybrid nanofluid.The wavy shaped enclosure is equipped with onequarter of a conducting solid cylinder.The system of equations resulting from the mathematical modeling of the physical problem in its dimensionless form is discretized via the higher-order Galerkin-based finite element method(GFEM).The dependency of various factors and their interrelationships affecting the hydro-thermal behavior and heat exchange rate are delineated.The numerical experiments reveal that the best heat transfer rate is achieved for the pseudo-plastic hybrid nanoliquid with high Rayleigh number and thermal conductivity ratio and low Hartmann number.Besides,the power-law index has a major effect in deteriorating the heat convection at high Rayleigh number.展开更多
Let G be a group and r（G） the set of element orders of G. Let k E 7（G） and mk be the number of elements of order k in G. Let （G） = {mk]k C Try（G）}. In this paper, we prove that L2（16） is recognizable by T^...Let G be a group and r（G） the set of element orders of G. Let k E 7（G） and mk be the number of elements of order k in G. Let （G） = {mk]k C Try（G）}. In this paper, we prove that L2（16） is recognizable by T^（L2（16））. In other words, we prove that if G is a group such that ^-^（G） =（L2（16）） = {1,255,272,544, 1088, 1920}, then G is isomorphic to L2（16）.展开更多
The famous strongly binary Goldbach’s conjecture asserts that every even number 2n ≥ 8 can always be expressible as a sum of two distinct odd prime numbers. We use a new approach to dealing with this conjecture. Spe...The famous strongly binary Goldbach’s conjecture asserts that every even number 2n ≥ 8 can always be expressible as a sum of two distinct odd prime numbers. We use a new approach to dealing with this conjecture. Specifically, we apply the element order prime graphs of alternating groups of degrees 2n and 2n −1 to characterize this conjecture, and present its six group-theoretic versions;and further prove that this conjecture is true for p +1 and p −1 whenever p ≥ 11 is a prime number.展开更多
This paper aims to treat a study of generators of the cyclic group of higher even, odd, and prime order for composition being multiplication. In fact we developed order of a group, order of element of a group and gene...This paper aims to treat a study of generators of the cyclic group of higher even, odd, and prime order for composition being multiplication. In fact we developed order of a group, order of element of a group and generators of the cyclic group in real numbers. Also we express cyclic and generators of the group for composition in real numbers. Here we discuss the higher order of groups in different types of order, and generators of the cyclic group which will give us practical knowledge to see the applications of the composition. In order to find out the order of an element am∈Gin which an=e= identity element, then find Highest Common Factor i.e. (H.C.F) of mand n. When Gis a finite group, every element must have finite order but the converse is false. There are infinite groups where each element has a finite order. There may be more than one generator of a cyclic group. Also every cyclic group is necessarily abelian. But show that every infinite cyclic group contains only two generators. Finally, we find out the generators of the cyclic group of higher even, odd and prime order in different types of the group for composition being multiplication.展开更多
This paper constructs the first mixed finite element for the linear elasticity problem in 3D using P3 polynomials for the stress and discontinuous P_(2) polynomials for the displacement on tetrahedral meshes under som...This paper constructs the first mixed finite element for the linear elasticity problem in 3D using P3 polynomials for the stress and discontinuous P_(2) polynomials for the displacement on tetrahedral meshes under some mild mesh conditions.The degrees of freedom of the stress space as well as the corresponding nodal basis are established by characterizing a space of certain piecewise constant symmetric matrices on a patch around each edge.Macro-element techniques are used to define a stable interpolation to prove the discrete inf-sup condition.Optimal convergence is obtained theoretically.展开更多
The well-known theorem of Dickson provides information on the element ordersof the groups PSL(2, q). In search of a converse to this, Refs. [1] and [2] proved thatif π_e.(G)=π_e(PSL(2, q)) and if q=2~m or q=3~m (m≥...The well-known theorem of Dickson provides information on the element ordersof the groups PSL(2, q). In search of a converse to this, Refs. [1] and [2] proved thatif π_e.(G)=π_e(PSL(2, q)) and if q=2~m or q=3~m (m≥2, q≠9), then G is isomorphic toPSL(2, q), where π_e(G) denotes the set of all orders of elements in G.展开更多
In this paper,we are concerned with the fast solvers for higher order edge finite element discretizations of Maxwell's equations.We present the preconditioners for the first family and second family of higher orde...In this paper,we are concerned with the fast solvers for higher order edge finite element discretizations of Maxwell's equations.We present the preconditioners for the first family and second family of higher order N′ed′elec element equations,respectively.By combining the stable decompositions of two kinds of edge finite element spaces with the abstract theory of auxiliary space preconditioning,we prove that the corresponding condition numbers of our preconditioners are uniformly bounded on quasi-uniform grids.We also present some numerical experiments to demonstrate the theoretical results.展开更多
For G a finite group,π_e(G)denotes the set of orders of elements in G.If Ω is a subset of the set of natural numbers,h(Ω)stands for the number of isomorphism classes of finite groups with the same set Ω of element...For G a finite group,π_e(G)denotes the set of orders of elements in G.If Ω is a subset of the set of natural numbers,h(Ω)stands for the number of isomorphism classes of finite groups with the same set Ω of element orders.We say that G is k-distinguishable if h(π_(G))=k<∞,otherwise G is called non-distinguishable.Usually,a 1-distinguishable group is called a characterizable group.It is shown that if M is a sporadic simple group different from M_(12),M_(22),J_2,He,Suz,M^cL and O'N, then Aut(M)is charaeterizable by its dement orders.It is also proved that if M is isomorphic to M_(12),M_(22),He,Suz or O'N,then h(π_e(Aut(M)))∈{1,∞}.展开更多
In this paper, we investigate numerical methods for high order differential equations. We propose new spectral and spectral element methods for high order problems with mixed inhomogeneous boundary conditions, and pro...In this paper, we investigate numerical methods for high order differential equations. We propose new spectral and spectral element methods for high order problems with mixed inhomogeneous boundary conditions, and prove their spectral accuracy by using the recent results on the Jacobi quasi-orthogonal approximation. Numerical results demonstrate the high accuracy of suggested algorithm, which also works well even for oscillating solutions.展开更多
In this paper,we present a new stabilized finite element method for transient Navier-Stokes equations with high Reynolds number based on the projection of the velocity and pressure.We use Taylor-Hood elements and the ...In this paper,we present a new stabilized finite element method for transient Navier-Stokes equations with high Reynolds number based on the projection of the velocity and pressure.We use Taylor-Hood elements and the equal order elements in space and second order difference in time to get the fully discrete scheme.The scheme is proven to possess the absolute stability and the optimal error estimates.Numerical experiments show that our method is effective for transient Navier-Stokes equations with high Reynolds number and the results are in good agreement with the value of subgrid-scale eddy viscosity methods,Pet ro-Galerkin finite element method and st reamline diffusion method.展开更多
Let φ be a homomorphism from a group H to a group Aut（N）. Denote by Hφ× N the semidirect product of N by H with homomorphism φ. This paper proves that： Let G be a finite nonsolvable group. If G has exactly ...Let φ be a homomorphism from a group H to a group Aut（N）. Denote by Hφ× N the semidirect product of N by H with homomorphism φ. This paper proves that： Let G be a finite nonsolvable group. If G has exactly 40 maximal order elements, then G is isomorphic to one of the following groups： （1） Z4φ×A5, kerφ = Z2; （2） D8φ ×A5, kerφ = Z2 ×Z2; （3） G/N = S5, N = Z（G） = Z2; （4） G/N = S5, N = Z2 ×Z2, N∩Z（G） = Z2.展开更多
文摘A high order boundary element method was developed for the complex velocity potential problem. The method ensures not only the continuity of the potential at the nodes of each element but also the velocity. It can be applied to a variety of velocity potential problems. The present paper, however, focused on its application to the problem of water entry of a wedge with varying speed. The continuity of the velocity achieved herein is particularly important for this kind of nonlinear free surface flow problem, because when the time stepping method is used, the free surface is updated through the velocity obtained at each node and the accuracy of the velocity is therefore crucial. Calculation was made for a case when the distance S that the wedge has travelled and time t follow the relationship s=Dtα, where D and α are constants, which is found to lead to a self similar flow field when the effect due to gravity is ignored.
基金This work has been supported by the Research Institute for Fundamental Sciences Tabriz,Iran.
文摘For any group G, denote byπe(G) the set of orders of elements in G. Given a finite group G, let h(πe (G)) be the number of isomorphism classes of finite groups with the same set πe(G) of element orders. A group G is called k-recognizable if h(πe(G)) = k <∞, otherwise G is called non-recognizable. Also a 1-recognizable group is called a recognizable (or characterizable) group. In this paper the authors show that the simple groups PSL(3,q), where 3 < q≡±2 (mod 5) and (6, (q-1)/2) = 1, are recognizable.
基金financially supported by the National Natural Science Foundation of China (Grant Nos.52271276,52271319,and 52201364)the Natural Science Foundation of Jiangsu Province (Grant No.BK20201006)。
文摘A higher order boundary element method(HOBEM)is presented for inviscid flow passing cylinders in bounded or unbounded domain.The traditional boundary integral equation is established with respect to the velocity potential and its normal derivative.In present work,a new integral equation is derived for the tangential velocity.The boundary is discretized into higher order elements to ensure the continuity of slope at the element nodes.The velocity potential is also expanded with higher order shape functions,in which the unknown coefficients involve the tangential velocity.The expansion then ensures the continuities of the velocity and the slope of the boundary at element nodes.Through extensive comparison of the results for the analytical solution of cylinders,it is shown that the present HOBEM is much more accurate than the conventional BEM.
基金the National Natural Science Foundation of China(10671184)
文摘In this paper, a new higher order Wilson element is presented, and the convergence is proved. Then the interpolation postprocessing technique is used to obtain the global superconvergence and posterior error estimate of higher accuracy of this new element for the Sobolev type equations.
文摘A new kind of material cast polyurethane elastomers (CPUE) is introduced to take the place of rubber on load bearing wheel for the first time. Based on load bearing wheel dimensions, material properties and operating conditions, the structure of wheel flange is optimized by zero order finite element method. A detailed three dimensional finite element model of flange of load bearing wheel is developed and utilized to optimize structure of wheel flange. Its service life, which is affected by flange structure parameter, is analyzed by comparing the optimization results with those of prototype of wheel. The results of optimization are presented and the stress field of load bearing wheel in optimal dimension obtained by using finite element analysis method is demonstrated. The finite element analysis and optimization results show that the CPUE load bearing wheel is feasible and suitable for the tracked vehicle and has a guiding value in practice of the weighting design of the whole tracked vehicle.
文摘This paper aims at treating a study on the order of every element for addition and multiplication composition in the higher order of groups for different algebraic structures as groups;order of a group and order of element of a group in real numbers. Here we discuss the higher order of groups in different types of order which will give us practical knowledge to see the applications of the addition and multiplication composition. If G is a finite group, n is a positive integer and a ⋴G, then the order of the products na. When G is a finite group, every element must have finite order. However, the converse is false: there are infinite groups where each element has finite order. For example, in the group of all roots of unity in C<sup>×</sup> each element has finite order. Finally, we find out the order of every element of a group in different types of higher order of group.
基金supported by the Fundamental Research Funds for the Central Universities and NPRP 08-691-2-289 grant from Qatar National Research Fund (QNRF)
文摘The finite element method （FEM） is employed to analyze the resonant oscillations of the liquid confined within multiple or an array of floating bodies with fully nonlinear boundary conditions on the free surface and the body surface in two dimensions. The velocity potentials at each time step are obtained through the FEM with 8-node quadratic shape functions. The finite element linear system is solved by the conjugate gradient （CG） method with a symmetric successive overelaxlation （SSOR） preconditioner. The waves at the open boundary are absorbed by the combination of the damping zone method and the Sommerfeld-Orlanski equation. Numerical examples are given by an array of floating wedge- shaped cylinders and rectangular cylinders. Results are provided for heave motions including wave elevations, profiles and hydrodynamic forces. Comparisons are made in several cases with the results obtained from the second order solution in the time domain. It is found that the wave amplitude in the middle region of the array is larger than those in other places, and the hydrodynamic force on a cylinder increases with the cylinder closing to the middle of the array.
文摘A fully nonlinear numerical wave tank (NWT) has been simulated by use of a three-dimensional higher order boundary element method (HOBEM) in the time domain. Within the frame of potential flow and the adoption of simply Rankine source, the resulting boundary integral equation is repeatedly solved at each time step and the fully nonlinear free surface boundary conditions are integrated with time to update its position and boundary values. A smooth technique is also adopted in order to eliminate the possible saw-tooth numerical instabilities. The incident wave at the uptank is given as theoretical wave in this paper. The outgoing waves are absorbed inside a damping zone by spatially varying artificial damping on the free surface at the wave tank end. The numerical results show that the NWT developed by these approaches has a high accuracy and good numerical stability.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1117136411271301)+2 种基金the Natural Science Foundation Project of CQ CSTC(Grant No.2014jcyjA00004)the Science and Technology Project of Chongqing Education Committee(Grant No.KJ1400520)the Foundation Project of Chongqing Normal University(Grant No.14XYY026)
文摘In this paper, we characterize some simple Ka-groups only by using the group order and largest element orders, where a simple K4-group is a simple group of order containing exactly four distinct primes.
文摘The present study concerns the modelization and numerical simulation for the heat and flow exchange characteristics in a novel configuration saturated with a nonNewtonian Ag-MgO hybrid nanofluid.The wavy shaped enclosure is equipped with onequarter of a conducting solid cylinder.The system of equations resulting from the mathematical modeling of the physical problem in its dimensionless form is discretized via the higher-order Galerkin-based finite element method(GFEM).The dependency of various factors and their interrelationships affecting the hydro-thermal behavior and heat exchange rate are delineated.The numerical experiments reveal that the best heat transfer rate is achieved for the pseudo-plastic hybrid nanoliquid with high Rayleigh number and thermal conductivity ratio and low Hartmann number.Besides,the power-law index has a major effect in deteriorating the heat convection at high Rayleigh number.
基金Supported by the National Natural Science Foundation of China (Grant No. 11171364)
文摘Let G be a group and r（G） the set of element orders of G. Let k E 7（G） and mk be the number of elements of order k in G. Let （G） = {mk]k C Try（G）}. In this paper, we prove that L2（16） is recognizable by T^（L2（16））. In other words, we prove that if G is a group such that ^-^（G） =（L2（16）） = {1,255,272,544, 1088, 1920}, then G is isomorphic to L2（16）.
文摘The famous strongly binary Goldbach’s conjecture asserts that every even number 2n ≥ 8 can always be expressible as a sum of two distinct odd prime numbers. We use a new approach to dealing with this conjecture. Specifically, we apply the element order prime graphs of alternating groups of degrees 2n and 2n −1 to characterize this conjecture, and present its six group-theoretic versions;and further prove that this conjecture is true for p +1 and p −1 whenever p ≥ 11 is a prime number.
文摘This paper aims to treat a study of generators of the cyclic group of higher even, odd, and prime order for composition being multiplication. In fact we developed order of a group, order of element of a group and generators of the cyclic group in real numbers. Also we express cyclic and generators of the group for composition in real numbers. Here we discuss the higher order of groups in different types of order, and generators of the cyclic group which will give us practical knowledge to see the applications of the composition. In order to find out the order of an element am∈Gin which an=e= identity element, then find Highest Common Factor i.e. (H.C.F) of mand n. When Gis a finite group, every element must have finite order but the converse is false. There are infinite groups where each element has a finite order. There may be more than one generator of a cyclic group. Also every cyclic group is necessarily abelian. But show that every infinite cyclic group contains only two generators. Finally, we find out the generators of the cyclic group of higher even, odd and prime order in different types of the group for composition being multiplication.
文摘This paper constructs the first mixed finite element for the linear elasticity problem in 3D using P3 polynomials for the stress and discontinuous P_(2) polynomials for the displacement on tetrahedral meshes under some mild mesh conditions.The degrees of freedom of the stress space as well as the corresponding nodal basis are established by characterizing a space of certain piecewise constant symmetric matrices on a patch around each edge.Macro-element techniques are used to define a stable interpolation to prove the discrete inf-sup condition.Optimal convergence is obtained theoretically.
文摘The well-known theorem of Dickson provides information on the element ordersof the groups PSL(2, q). In search of a converse to this, Refs. [1] and [2] proved thatif π_e.(G)=π_e(PSL(2, q)) and if q=2~m or q=3~m (m≥2, q≠9), then G is isomorphic toPSL(2, q), where π_e(G) denotes the set of all orders of elements in G.
基金the National Natural Science Foundation of China(Grant Nos.10771178,10676031)the National Key Basic Research Program of China(973Program)(Grant No.2005CB321702)the Key Project of Chinese Ministry of Education and Scientific Research Fund of Hunan Provincial Education Department(Grant Nos.208093,07A068)
文摘In this paper,we are concerned with the fast solvers for higher order edge finite element discretizations of Maxwell's equations.We present the preconditioners for the first family and second family of higher order N′ed′elec element equations,respectively.By combining the stable decompositions of two kinds of edge finite element spaces with the abstract theory of auxiliary space preconditioning,we prove that the corresponding condition numbers of our preconditioners are uniformly bounded on quasi-uniform grids.We also present some numerical experiments to demonstrate the theoretical results.
基金This work has been partially sopported by the Research Institute for Fundamental Sciences Tabriz,Iran
文摘For G a finite group,π_e(G)denotes the set of orders of elements in G.If Ω is a subset of the set of natural numbers,h(Ω)stands for the number of isomorphism classes of finite groups with the same set Ω of element orders.We say that G is k-distinguishable if h(π_(G))=k<∞,otherwise G is called non-distinguishable.Usually,a 1-distinguishable group is called a characterizable group.It is shown that if M is a sporadic simple group different from M_(12),M_(22),J_2,He,Suz,M^cL and O'N, then Aut(M)is charaeterizable by its dement orders.It is also proved that if M is isomorphic to M_(12),M_(22),He,Suz or O'N,then h(π_e(Aut(M)))∈{1,∞}.
文摘In this paper, we investigate numerical methods for high order differential equations. We propose new spectral and spectral element methods for high order problems with mixed inhomogeneous boundary conditions, and prove their spectral accuracy by using the recent results on the Jacobi quasi-orthogonal approximation. Numerical results demonstrate the high accuracy of suggested algorithm, which also works well even for oscillating solutions.
基金We thank Dr.Chen Gang for the great help to the numerical part of this paper.This research was supported by the Natural Science Foundation of China(No.11271273)Major Project of Education Department in Sichan(No.18ZA0276).
文摘In this paper,we present a new stabilized finite element method for transient Navier-Stokes equations with high Reynolds number based on the projection of the velocity and pressure.We use Taylor-Hood elements and the equal order elements in space and second order difference in time to get the fully discrete scheme.The scheme is proven to possess the absolute stability and the optimal error estimates.Numerical experiments show that our method is effective for transient Navier-Stokes equations with high Reynolds number and the results are in good agreement with the value of subgrid-scale eddy viscosity methods,Pet ro-Galerkin finite element method and st reamline diffusion method.
基金the Natural of Chongqing Three Gorge University(No.2007-sxxyyb-01)
文摘Let φ be a homomorphism from a group H to a group Aut（N）. Denote by Hφ× N the semidirect product of N by H with homomorphism φ. This paper proves that： Let G be a finite nonsolvable group. If G has exactly 40 maximal order elements, then G is isomorphic to one of the following groups： （1） Z4φ×A5, kerφ = Z2; （2） D8φ ×A5, kerφ = Z2 ×Z2; （3） G/N = S5, N = Z（G） = Z2; （4） G/N = S5, N = Z2 ×Z2, N∩Z（G） = Z2.
