High Order Mixed Finite Elements with Mass Lumping for Elasticity on Triangular Grids

作     者：Yan Yang Xiaoping Xie 

作者机构：School of SciencesSouthwest Petroleum UniversityChengdu 610500China School of MathematicsSichuan UniversityChengdu 610064China 

出 版 物：《Numerical Mathematics(Theory,Methods and Applications)》 (高等学校计算数学学报（英文版）)

年 卷 期：2022年第15卷第1期

页      面：227-250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 in part by the National Natural Science Foundation of China(Grants 11771312 12171340). 

主　　题：Linear elasticity mixed finite element mass lumping error estimate 

摘      要：A family of conforming mixed finite elements with mass lumping on triangular grids are presented for linear elasticity.The stress field is approximated by symmetric H(div)−Pk(k≥3)polynomial tensors enriched with higher order bubbles so as to allow mass lumping,and the displacement field is approximated by C−1−Pk−1 polynomial vectors enriched with higher order terms.For both the proposed mixed elements and their mass lumping schemes,optimal error estimates are derived for the stress and displacement in H(div)norm and L 2 norm,respectively.Numerical results confirm the theoretical analysis.