A stabilizer-free C^(0) weak Galerkin method for the biharmonic equations

作     者：Peng Zhu Shenglan Xie Xiaoshen Wang 

作者机构：College of Data ScienceJiaxing UniversityJiaxing 314001China College of Information EngineeringJiaxing Nanhu UniversityJiaxing 314001China Department of MathematicsUniversity of Arkansas at Little RockLittle RockAR 72204USA 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2023年第66卷第3期

页      面：627-646页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：supported by Zhejiang Provincial Natural Science Foundation of China(Grant No.LY19A010008) National Natural Science Foundation of China(Grant No.12071184)。 

主　　题：weak Galerkin finite element method weak Laplacian biharmonic equations 

摘      要：In this article, we present and analyze a stabilizer-free C^(0)weak Galerkin(SF-C^(0)WG) method for solving the biharmonic problem. The SF-C^(0)WG method is formulated in terms of cell unknowns which are C^(0)continuous piecewise polynomials of degree k + 2 with k≥0 and in terms of face unknowns which are discontinuous piecewise polynomials of degree k + 1. The formulation of this SF-C^(0)WG method is without the stabilized or penalty term and is as simple as the C1conforming finite element scheme of the biharmonic problem. Optimal order error estimates in a discrete H^(2)-like norm and the H^(1)norm for k≥0 are established for the corresponding WG finite element solutions. Error estimates in the L^(2)norm are also derived with an optimal order of convergence for k 0 and sub-optimal order of convergence for k = 0. Numerical experiments are shown to confirm the theoretical results.