In this article,some high-order local discontinuous Galerkin(LDG)schemes based on some second-order θ approximation formulas in time are presented to solve a two-dimen-sional nonlinear fractional diffusion equation.T...In this article,some high-order local discontinuous Galerkin(LDG)schemes based on some second-order θ approximation formulas in time are presented to solve a two-dimen-sional nonlinear fractional diffusion equation.The unconditional stability of the LDG scheme is proved,and an a priori error estimate with O(h^(k+1)+At^(2))is derived,where k≥0 denotes the index of the basis function.Extensive numerical results with Q^(k)(k=0,1,2,3)elements are provided to confirm our theoretical results,which also show that the second-order convergence rate in time is not impacted by the changed parameter θ.展开更多
In this work,a new numerical scheme is proposed for thermal/isothermal incompressible viscous flows based on operator splitting.Unique solvability and stability analysis are presented.Some numerical result are given,w...In this work,a new numerical scheme is proposed for thermal/isothermal incompressible viscous flows based on operator splitting.Unique solvability and stability analysis are presented.Some numerical result are given,which show that the proposed scheme is highly efficient for the thermal/isothermal incompressible viscous flows.展开更多
基金This work is supported by the National Natural Science Foundation of China(11661058,11761053)the Natural Science Foundation of Inner Mongolia(2017MS0107)the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(NJYT-17-A07).
文摘In this article,some high-order local discontinuous Galerkin(LDG)schemes based on some second-order θ approximation formulas in time are presented to solve a two-dimen-sional nonlinear fractional diffusion equation.The unconditional stability of the LDG scheme is proved,and an a priori error estimate with O(h^(k+1)+At^(2))is derived,where k≥0 denotes the index of the basis function.Extensive numerical results with Q^(k)(k=0,1,2,3)elements are provided to confirm our theoretical results,which also show that the second-order convergence rate in time is not impacted by the changed parameter θ.
基金The work of the first author was supported by the grants of the National Natural Science Foundation of China(10971165,10901122,11001216,11026051).
文摘In this work,a new numerical scheme is proposed for thermal/isothermal incompressible viscous flows based on operator splitting.Unique solvability and stability analysis are presented.Some numerical result are given,which show that the proposed scheme is highly efficient for the thermal/isothermal incompressible viscous flows.
