A new method for estimating the posterior error of linear triangular element is presented. According to the specified accuracy, the element size and node spacing function of adaptive h-version mesh refinement are pred...A new method for estimating the posterior error of linear triangular element is presented. According to the specified accuracy, the element size and node spacing function of adaptive h-version mesh refinement are predicted. The main domain is divided by the isolines of node spacing into subregions in which mesh regeneration is realized. This remeshing refinement process implements mesh subdivision and mesh de-refinement in onecycle.展开更多
This paper focuses on constructing the adaptive analysis model based on the Finite Element Method(FEM)with an unstructured mesh,which includes taking full advantage of the two-dimensional triangle’s ability to discre...This paper focuses on constructing the adaptive analysis model based on the Finite Element Method(FEM)with an unstructured mesh,which includes taking full advantage of the two-dimensional triangle’s ability to discretize any complex model.The error indicator and h-type refinement scheme for FEM has been presented by providing a simple error indicator based on the difference value of nodal fundamental physical variables.It provides an effective measure of the error in the numerical solution,which can lead to an adaptive refinement scheme,determining the optimal location of new inserted nodes that are mainly distributed in the local high stress gradient domain.A numerical experiment is presented to demonstrate that the proposed error indicator reasonably tracks the distribution of the true error,and the effectiveness of the proposed adaptive analysis procedure,which achieves significantly higher convergence rates compared to the uniform mesh.展开更多
Based on the concept of the constitutive relation error along with the residuals of both the origin and the dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed. It lead...Based on the concept of the constitutive relation error along with the residuals of both the origin and the dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed. It leads to the high quality locM error bounds in the problem of the direct-solution steady-state dynamic analysis with a frequency-domain finite element, which involves the enrichments with plural variable basis functions. The solution of the steady-state dynamic procedure calculates the harmonic response directly in terms of the physical degrees of freedom in the model, which uses the mass, damping, and stiffness matrices of the system. A three-dimensional finite element example is carried out to illustrate the computational procedures.展开更多
This paper studies convergence analysis of an adaptive finite element algorithm for numerical estimation of some unknown distributed flux in a stationary heat conduction system,namely recovering the unknown Neumann da...This paper studies convergence analysis of an adaptive finite element algorithm for numerical estimation of some unknown distributed flux in a stationary heat conduction system,namely recovering the unknown Neumann data on interior inaccessible boundary using Dirichlet measurement data on outer accessible boundary.Besides global upper and lower bounds established in[23],a posteriori local upper bounds and quasi-orthogonality results concerning the discretization errors of the state and adjoint variables are derived.Convergence and quasi-optimality of the proposed adaptive algorithm are rigorously proved.Numerical results are presented to illustrate the quasi-optimality of the proposed adaptive method.展开更多
An h-adaptive meshless method is proposed in this paper. The error estimation is based on local fit technology, usually confined to Voronoi Cells. The error is achieved by comparison of the computational results with ...An h-adaptive meshless method is proposed in this paper. The error estimation is based on local fit technology, usually confined to Voronoi Cells. The error is achieved by comparison of the computational results with smoothed ones, which are projected with Taylor series. Voronoi Cells are introduced not only for integration of potential energy but also for guidance of refinement. New nodes are placed within those cells with high estimated error. At the end of the paper, two numerical examples with severe stress gradient are analyzed. Through adaptive analysis accurate results are obtained at critical subdomains, which validates the efficiency of the method.展开更多
文摘A new method for estimating the posterior error of linear triangular element is presented. According to the specified accuracy, the element size and node spacing function of adaptive h-version mesh refinement are predicted. The main domain is divided by the isolines of node spacing into subregions in which mesh regeneration is realized. This remeshing refinement process implements mesh subdivision and mesh de-refinement in onecycle.
基金supported by the Hunan Provincial Natural Science Foundation of China.(Grant No.2023JJ50222).
文摘This paper focuses on constructing the adaptive analysis model based on the Finite Element Method(FEM)with an unstructured mesh,which includes taking full advantage of the two-dimensional triangle’s ability to discretize any complex model.The error indicator and h-type refinement scheme for FEM has been presented by providing a simple error indicator based on the difference value of nodal fundamental physical variables.It provides an effective measure of the error in the numerical solution,which can lead to an adaptive refinement scheme,determining the optimal location of new inserted nodes that are mainly distributed in the local high stress gradient domain.A numerical experiment is presented to demonstrate that the proposed error indicator reasonably tracks the distribution of the true error,and the effectiveness of the proposed adaptive analysis procedure,which achieves significantly higher convergence rates compared to the uniform mesh.
基金Project supported by the National Natural Science Foundation of China (No. 10876100)
文摘Based on the concept of the constitutive relation error along with the residuals of both the origin and the dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed. It leads to the high quality locM error bounds in the problem of the direct-solution steady-state dynamic analysis with a frequency-domain finite element, which involves the enrichments with plural variable basis functions. The solution of the steady-state dynamic procedure calculates the harmonic response directly in terms of the physical degrees of freedom in the model, which uses the mass, damping, and stiffness matrices of the system. A three-dimensional finite element example is carried out to illustrate the computational procedures.
基金supported by the NSFC grant(No.11101386)the Fundamental Research Funds for the Central Universities of China+1 种基金supported by the NSFC grants(No.11201453 and 91130022)supported by the NSFC grants(No.11101414 and 91130026).
文摘This paper studies convergence analysis of an adaptive finite element algorithm for numerical estimation of some unknown distributed flux in a stationary heat conduction system,namely recovering the unknown Neumann data on interior inaccessible boundary using Dirichlet measurement data on outer accessible boundary.Besides global upper and lower bounds established in[23],a posteriori local upper bounds and quasi-orthogonality results concerning the discretization errors of the state and adjoint variables are derived.Convergence and quasi-optimality of the proposed adaptive algorithm are rigorously proved.Numerical results are presented to illustrate the quasi-optimality of the proposed adaptive method.
基金Project supported by the National Natural Science Foundation of China (No. 50175060).
文摘An h-adaptive meshless method is proposed in this paper. The error estimation is based on local fit technology, usually confined to Voronoi Cells. The error is achieved by comparison of the computational results with smoothed ones, which are projected with Taylor series. Voronoi Cells are introduced not only for integration of potential energy but also for guidance of refinement. New nodes are placed within those cells with high estimated error. At the end of the paper, two numerical examples with severe stress gradient are analyzed. Through adaptive analysis accurate results are obtained at critical subdomains, which validates the efficiency of the method.
