A family of high-order accuracy explict difference schemes for solving 3-dimension parabolic P. D. E. is constructed. The stability condition is r = Deltat/Deltax(2) Deltat/Deltay(2) = Deltat/Deltaz(2) < 1/2 ,and t...A family of high-order accuracy explict difference schemes for solving 3-dimension parabolic P. D. E. is constructed. The stability condition is r = Deltat/Deltax(2) Deltat/Deltay(2) = Deltat/Deltaz(2) < 1/2 ,and the truncation error is 0(<Delta>t(2) + Deltax(4)).展开更多
A second order accurate method in the infinity norm is proposed for general three dimensional anisotropic elliptic interface problems in which the solution and its derivatives,the coefficients,and source terms all can...A second order accurate method in the infinity norm is proposed for general three dimensional anisotropic elliptic interface problems in which the solution and its derivatives,the coefficients,and source terms all can have finite jumps across one or several arbitrary smooth interfaces.The method is based on the 2D finite element-finite difference(FEFD)method but with substantial differences in method derivation,implementation,and convergence analysis.One of challenges is to derive 3D interface relations since there is no invariance anymore under coordinate system transforms for the partial differential equations and the jump conditions.A finite element discretization whose coefficient matrix is a symmetric semi-positive definite is used away from the interface;and the maximum preserving finite difference discretization whose coefficient matrix part is an M-matrix is constructed at irregular elements where the interface cuts through.We aim to get a sharp interface method that can have second order accuracy in the point-wise norm.We show the convergence analysis by splitting errors into several parts.Nontrivial numerical examples are presented to confirm the convergence analysis.展开更多
基金Supported by Natural Science Foundation of Xinjiang AutonomousRegion (200821182 )Science and Technology Research andDevelopment Program of Xinjiang Autonomous Region (200841122)+1 种基金Science and Technology Planning Project of Xinjiang AutonomousRegion (200711104)the National Transgenic Major Program~~
文摘A family of high-order accuracy explict difference schemes for solving 3-dimension parabolic P. D. E. is constructed. The stability condition is r = Deltat/Deltax(2) Deltat/Deltay(2) = Deltat/Deltaz(2) < 1/2 ,and the truncation error is 0(<Delta>t(2) + Deltax(4)).
基金Zhilin Li is partially supported by Simon’s grant 633724.Xiufang Feng is partially supported by CNSF Grant No.11961054Baiying Dong is partially supported by Ningxia Natural Science Foundation of China Grant No.2021AAC03234.
文摘A second order accurate method in the infinity norm is proposed for general three dimensional anisotropic elliptic interface problems in which the solution and its derivatives,the coefficients,and source terms all can have finite jumps across one or several arbitrary smooth interfaces.The method is based on the 2D finite element-finite difference(FEFD)method but with substantial differences in method derivation,implementation,and convergence analysis.One of challenges is to derive 3D interface relations since there is no invariance anymore under coordinate system transforms for the partial differential equations and the jump conditions.A finite element discretization whose coefficient matrix is a symmetric semi-positive definite is used away from the interface;and the maximum preserving finite difference discretization whose coefficient matrix part is an M-matrix is constructed at irregular elements where the interface cuts through.We aim to get a sharp interface method that can have second order accuracy in the point-wise norm.We show the convergence analysis by splitting errors into several parts.Nontrivial numerical examples are presented to confirm the convergence analysis.
