2020/09/17 by Xiu Ye, Ye, Xiu, Shangyou Zhang +1
Engineering · Mathematics · #65N15 #65N30 #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2009.08536
openalex publication_date 2020/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A weak Galerkin (WG) finite element method without stabilizers was introduced in [J. Comput. Appl. Math., 371 (2020). arXiv:1906.06634] on polytopal mesh. Then it was improved in [arXiv:2008.13631] with order one superconvergence. The goal of this paper is to develop a new stabilizer free WG method on polytopal mesh. This method has convergence rates two orders higher than the optimal convergence rates for the corresponding WG solution in both an energy norm and the L2 norm. The numerical examples are tested for low and high order elements in two and three dimensional spaces.