Mesh Conditions of the Preserving-Maximum-Principle Linear Finite Volume Element Method for Anisotropic Diffusion-Convection-Reaction Equations  

作　　者：Lei LIN Jun-liang LV Jing-yan YUE Guang-wei YUAN 

机构地区：[1]School of Mathematics,Jilin University,Changchun 130012,China [2]Laboratory of Computational Physics,Institute of Applied Physics and Computational Mathematics,Beijing 100088,China

出　　处：《Acta Mathematicae Applicatae Sinica》2023年第3期707-732,共26页应用数学学报（英文版）

基　　金：the National Natural Science Foundation of China(No.11301033,11971069 and 12271209);the Natural Science Foundation of Jilin Province(No.20200201259JC);Jilin Province Science and Technology Plan Development Project(No.20210201078GX)。

摘　　要：We develop mesh conditions for linear finite volume element approximations of anisotropic diffusionconvectionreaction problems to satisfy the discrete maximum principle.We obtain the sufficient conditions to gurantee the both upper and lower bounds of the numerical solution when each angle of arbitrary triangle is O(∥q∥_∞h+∥g∥_∞h~2)-acute and h is small enough,where h denotes the mesh size,q and g are coefficients of the convection and reaction terms,respectively.To deal with the convection-dominated problems,we use the upwind triangle technique.For such scheme,the mesh condition can be sharper to O(∥g∥_∞h~2)-acute.Some numerical examples are presented to demonstrate the theoretical results.

关 键 词：anisotropic diffusion-convection-reaction equation finite volume element method discrete maximum principle 

分 类 号：O241.82[理学—计算数学]