Four-Order Superconvergent Weak Galerkin Methods for the Biharmonic Equation on Triangular Meshes

作     者：Xiu Ye Shangyou Zhang Xiu Ye;Shangyou Zhang

作者机构：Department of MathematicsUniversity of Arkansas at Little RockLittle RockAR72204USA Department of Mathematical SciencesUniversity of DelawareNewarkDE19716USA 

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：2023年第5卷第4期

页      面：1323-1338页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Finite element Weak Hessian Weak Galerkin(WG) Biharmonic equation Triangular mesh 

摘      要：A stabilizer-free weak Galerkin(SFWG)finite element method was introduced and analyzed in Ye and Zhang(SIAM ***.58:2572–2588,2020)for the biharmonic equation,which has an ultra simple finite element *** work is a continuation of our investigation of the SFWG method for the biharmonic *** new SFWG method is highly accurate with a convergence rate of four orders higher than the optimal order of convergence in both the energy norm and the L^(2)norm on triangular *** new method also keeps the formulation that is symmetric,positive definite,and ***-order superconvergence error estimates are proved for the corresponding SFWG finite element solutions in a discrete H^(2)*** of four orders in the L^(2)norm is also derived for k≥3,where k is the degree of the approximation *** postprocessing is proved to lift a P_(k)SFWG solution to a P_(k+4)solution elementwise which converges at the optimal *** examples are tested to verify the theor ies.