Two‐grid weak Galerkin method for semilinear elliptic differential equations. (25th June 2022) - Chen, Luoping; Wu, Fanyun; Zeng, Guoyan
Abstract : In this paper, we investigate a two‐grid weak Galerkin method for semilinear elliptic differential equations. The method mainly contains two steps. First, we solve the semilinear elliptic equation on the coarse mesh with mesh size H $$ H $$, then, we use the coarse mesh solution as an initial guess to linearize the semilinear equation on the fine mesh, that is, on the fine mesh (with mesh size h $$ h $$ ), we only need to solve a linearized system. Theoretical analysis shows that when the exact solution u $$ u $$ has sufficient regularity and h = H 2 $$ h=H^2 $$, the two‐grid weak Galerkin method achieves the same convergence accuracy as weak Galerkin method. Several examples are given to verify the theoretical results.