Adv. Appl. Math. Mech., 17 (2025), pp. 681-705.
Published online: 2025-03
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In this article, we study a parabolic equation with both nonlinear time-derivative term and nonlinear diffusion term by the finite volume element method. The optimal error estimate in $H^1$-norm is proved for fully discrete scheme. The suboptimal error estimate in $L^2$-norm is proved both for semi-discrete scheme and fully discrete scheme. We prove the existence of solution for the fully discrete scheme. Numerical results show the effectiveness of our method.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2022-0258}, url = {http://global-sci.org/intro/article_detail/aamm/23894.html} }In this article, we study a parabolic equation with both nonlinear time-derivative term and nonlinear diffusion term by the finite volume element method. The optimal error estimate in $H^1$-norm is proved for fully discrete scheme. The suboptimal error estimate in $L^2$-norm is proved both for semi-discrete scheme and fully discrete scheme. We prove the existence of solution for the fully discrete scheme. Numerical results show the effectiveness of our method.