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, 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), 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.
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.
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