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Volume 17, Issue 3
Finite Volume Element Method for a Nonlinear Parabolic Equation

Yanwei Du & Yonghai Li

Adv. Appl. Math. Mech., 17 (2025), pp. 681-705.

Published online: 2025-03

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  • Abstract

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.

  • AMS Subject Headings

65N08, 65N15

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COPYRIGHT: © Global Science Press

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@Article{AAMM-17-681, author = {Du , Yanwei and Li , Yonghai}, title = {Finite Volume Element Method for a Nonlinear Parabolic Equation}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2025}, volume = {17}, number = {3}, pages = {681--705}, abstract = {

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} }
TY - JOUR T1 - Finite Volume Element Method for a Nonlinear Parabolic Equation AU - Du , Yanwei AU - Li , Yonghai JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 681 EP - 705 PY - 2025 DA - 2025/03 SN - 17 DO - http://doi.org/10.4208/aamm.OA-2022-0258 UR - https://global-sci.org/intro/article_detail/aamm/23894.html KW - Nonlinear parabolic equation, error estimate, finite volume element method. AB -

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.

Du , Yanwei and Li , Yonghai. (2025). Finite Volume Element Method for a Nonlinear Parabolic Equation. Advances in Applied Mathematics and Mechanics. 17 (3). 681-705. doi:10.4208/aamm.OA-2022-0258
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