A Posteriori Error Estimate of Weak Galerkin FEM for Stokes Problem Using Auxiliary Subspace Techniques

查看全文 作　　者：Jiachuan [1]Zhang;Ran [2]Zhang;Xiaoshen [3]Wang 机构地区：[1]School of Physical and Mathematical Sciences,Nanjing Tech University,Nanjing 211816,China;[2]School of Mathematics,Jilin University,Changchun 130012,China;[3]Department of Mathematics and Statistics,University of Arkansas at Little Rock,Arkansas 72204,USA. 出　　处：《Communications in Computational Physics》索引2023年第33卷第2期,共27页 基　　金：the Natural Science Foundation of Jiangsu Province(No.BK20210540);the Natural Science Foundation of The Jiangsu Higher Education Institutions of China(No.21KJB110015);the National Key Research and Development Program of China(grant no.2020YFA0713601). 摘　　要：Based on the auxiliary subspace techniques,a posteriori error estimator of nonconforming weak Galerkin finite element method(WGFEM)for Stokes problem in two and three dimensions is presented.Without saturation assumption,we prove that the WGFEM approximation error is bounded by the error estimator up to an oscillation term.The computational cost of the approximation and the error problems is considered in terms of size and sparsity of the system matrix.To reduce the computational cost of the error problem,an equivalent error problem is constructed by using diagonalization techniques,which needs to solve only two diagonal linear algebraic systems corresponding to the degree of freedom(d.o.f)to get the error estimator.Numerical experiments are provided to demonstrate the effectiveness and robustness of the a posteriori error estimator. 关 键 词：Auxiliary subspace techniques diagonalization techniques weak Galerkin A posteriori error estimate Stokes problem.