A Robust Modified Weak Galerkin Finite Element Method for Reaction-Diffusion Equations
反应扩散方程的稳健修正弱伽辽金有限元方法
反応拡散方程式のためのロバストな修正された弱いガラーキン有限要素法
반응-확산 방정식을 위한 강력한 수정된 Weak Galerkin 유한 요소 방법
Un método de elementos finitos de Galerkin débil modificado robusto para ecuaciones de reacción-difusión
Une méthode robuste des éléments finis de Galerkin faible modifié pour les équations de réaction-diffusion
Робастный модифицированный слабый метод конечных элементов Галеркина для уравнений реакции-диффузии
¹ School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang 524048, Guangdong, P.R. China
广东 湛江 岭南师范大学数学与统计学院
² School of Mathematical Science, South China Normal University, Guangzhou 510631, Guangdong, P.R. China
中国 广东 广州 华南师范大学数学科学学院
³ Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan, P.R. China
中国 湖南 湘潭 湘潭大学数学与计算科学学院 科学工程计算与数值仿真湖南省重点实验室
Numerical Mathematics: Theory, Methods and Applications, 4 October 2021
Abstract
In this paper, a robust modified weak Galerkin (MWG) finite element method for reaction-diffusion equations is proposed and investigated. An advantage of this method is that it can deal with the singularly perturbed reaction-diffusion equations. Another advantage of this method is that it produces fewer degrees of freedom than the traditional WG method by eliminating the element boundaries freedom.
It is worth pointing out that, in our method, the test functions space is the same as the finite element space, which is helpful for the error analysis. Optimalorder error estimates are established for the corresponding numerical approximation in various norms. Some numerical results are reported to confirm the theory.
