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 semi-linear elliptic equation on the
coarse mesh with mesh size H, then, we use the coarse mesh solution as a
initial guess to linearize the semilinear equation on the fine mesh,
i.e., on the fine mesh (with mesh size $h$), we only need to solve a
linearized system. Theoretical analysis shows that when the exact
solution u has sufficient regularity and $h=H^2$, the two-grid weak
Galerkin method achieves the same convergence accuracy as weak Galerkin
method. Several examples are given to verify the theoretical results.