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 - <p style="text-align: justify;">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.</p>