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 ( h 1 / 2 ) . 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.