East Asian J. Appl. Math., 11 (2021), pp. 540-559.
Published online: 2021-05
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A two-grid finite volume element algorithm based on Crank-Nicolson scheme for nonlinear parabolic equations is proposed. In this method, the nonlinear problem is solved on a coarse grid of size $H$ and a linear problem is considered on a fine grid of size $h$ by using the coarse-grid solution and one Newton iteration. This helps to improve the computing efficiency while keeping the accuracy. It is proved that the two-grid method can achieve asymptotically optimal error estimates in spaces and second order accuracy in time. Numerical results are consistent with the theoretical findings.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.090820.311220}, url = {http://global-sci.org/intro/article_detail/eajam/19140.html} }A two-grid finite volume element algorithm based on Crank-Nicolson scheme for nonlinear parabolic equations is proposed. In this method, the nonlinear problem is solved on a coarse grid of size $H$ and a linear problem is considered on a fine grid of size $h$ by using the coarse-grid solution and one Newton iteration. This helps to improve the computing efficiency while keeping the accuracy. It is proved that the two-grid method can achieve asymptotically optimal error estimates in spaces and second order accuracy in time. Numerical results are consistent with the theoretical findings.