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

作　　者：Xiu Ye Shangyou Zhang 

机构地区：[1]Department of Mathematics,University of Arkansas at Little Rock,Little Rock,AR,72204,USA [2]Department of Mathematical Sciences,University of Delaware,Newark,DE,19716,USA

出　　处：《Communications on Applied Mathematics and Computation》2023年第4期1323-1338,共16页应用数学与计算数学学报（英文）

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

关 键 词：Finite element Weak Hessian Weak Galerkin(WG) Biharmonic equation Triangular mesh 

分 类 号：O17[理学—数学]