TY - JOUR
T1 - A Posteriori Error Estimate of Weak Galerkin FEM for Stokes Problem Using Auxiliary Subspace Techniques
AU - Zhang , Jiachuan
AU - Zhang , Ran
AU - Wang , Xiaoshen
JO - Communications in Computational Physics
VL - 2
SP - 511
EP - 537
PY - 2023
DA - 2023/03
SN - 33
DO - http://doi.org/10.4208/cicp.OA-2022-0207
UR - https://global-sci.org/intro/article_detail/cicp/21498.html
KW - Auxiliary subspace techniques, diagonalization techniques, weak Galerkin, A posteriori error estimate, Stokes problem.
AB - <p style="text-align: justify;">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.</p>