A Posteriori Error Estimate of Weak Galerkin FEM for Stokes Problem Using Auxiliary Subspace Techniques (Communications in Computational Physics, 2023)
Based on the auxiliary subspace techniques, a posteriori error estimator ofnonconforming weak Galerkin finite element method (WGFEM) for Stokes problemin two and three dimensions is presented. Without saturation assumption, we provethat 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 isconsidered 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 usingdiagonalization techniques, which needs to solve only two diagonal linear algebraicsystems corresponding to the degree of freedom $(d.o.f)$ to get the error estimator. Numerical experiments are provided to demonstrate the effectiveness and robustness ofthe a posteriori error estimator.