A posteriori error estimate of weak Galerkin fem for second order elliptic problem with mixed boundary condition

Abstract

<p style='text-indent:20px;'>A reliable and efficient a posteriori error estimator is presented for a weak Galerkin finite element method without stabilizer for the second order elliptic equation with mixed boundary conditions. The upper bound of the estimator is proved by Helmholtz decomposition technique and lower bound is hold naturally. The performance of the estimator is illustrated by numerical experiments.