(Peer-Reviewed) A Robust Modified Weak Galerkin Finite Element Method for Reaction-Diffusion Equations
Guanrong Li 李观荣 ¹, Yanping Chen 陈艳萍 ², Yunqing Huang 黄云清 ³
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
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.
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