Two-grid weak Galerkin finite element method for nonlinear parabolic equations

In this paper, we propose a two-grid algorithm for solving parabolic equation with nonlinear compressibility coefficient, spatially discretized by the weak Galerkin finite element method. The optimal error estimates are established. We further show that both grid solutions can achieve the same accuracy as long as the grid size satisfies $H=O\left(h^{1/2}\right)$. Compared with Newton iteration, the two-grid algorithm could greatly reduce the computational cost. We verify the effectiveness of the algorithm by performing numerical experiments.