A Weak Galerkin Harmonic Finite Element Method for Laplace Equation

作     者：Ahmed Al-Taweel Yinlin Dong Saqib Hussain Xiaoshen Wang Ahmed Al-Taweel;Yinlin Dong;Saqib Hussain;Xiaoshen Wang

作者机构：Department of Mathematics and StatisticsUniversity of Arkansas at Little RockLittle RockAR 72204USA Department of MathematicsUniversity of Central ArkansasConwayAR 72035USA Department of Mathematics and PhysicsTexas A&M International UniversityLaredoTX 78041USA 

出 版 物：《Communications on Applied Mathematics and Computation》 (应用数学与计算数学学报（英文）)

年 卷 期：2021年第3卷第3期

页      面：527-543页

核心收录：

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 070101[理学-基础数学] 

主　　题：Harmonic polynomial Weak Galerkin finite element Laplace equation 

摘      要：In this article,a weak Galerkin finite element method for the Laplace equation using the harmonic polynomial space is proposed and *** idea of using the P_(k)-harmonic polynomial space instead of the full polynomial space P_(k)is to use a much smaller number of basis functions to achieve the same accuracy when k≥*** optimal rate of convergence is derived in both H^(1)and L^(2)*** experiments have been conducted to verify the theoretical error *** addition,numerical comparisons of using the P_(2)-harmonic polynomial space and using the standard P_(2)polynomial space are presented.