A posteriori error estimates of two-grid weak Galerkin methods for semilinear elliptic differential equations

Abstract

In this paper, we investigate the residual-based a posteriori error estimates of two-grid weak Galerkin (WG) methods for second order semilinear elliptic partial differential equations (PDEs). First, we propose two different two-grid weak Galerkin methods for the model problem and then establish a posteriori error estimators of the two-grid weak Galerkin methods. Theoretical analysis is given to prove the reliability and efficiency of the error estimators. We mainly study the lowest order case of WG element (Pj(T),Pℓ(∂T),RTj(T)) with j=ℓ=0[19]. Numerical experiments are provided to confirm the theoretical results.