Abstract
In this paper, we present a two-grid virtual element method to solve the nonlinear parabolic problem. The nonlinear terms f(u) are approximated by using the L2 orthogonal projection, and the fine-grid discrete form is enhanced by Newton iteration. We first prove the H1-norm error estimate for the fully discrete problem. Furthermore, the a priori error estimates of two-grid method in the L2- and H1-norms achieve the optimal order O(hk+1+H2k+τ) and O(hk+H2k+τ), respectively. Finally, we used two numerical examples to validate our two-grid algorithm, which is consistent with our theoretical results.
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