一维非线性抛物问题两层网格有限体积元逼近

A Two-Grid Finite Volume Element Approximation for One-Dimensional Nonlinear Parabolic Equations

该文主要研究一维非线性抛物问题两层网格有限体积元逼近.对一维非线性抛物问题有限体积元解的存在性进行了讨论,给出了最优阶L^2-模和H^1-模误差估计结果,并研究了其两层网格算法.证明了当粗细网格步长满足h=O(H^2)时两层网格算法具有最优阶H^1-模误差估计.数值算例验证了理论结果.

In this paper, a two-grid finite volume element approximation for one-dimensional nonlinear parabolic equations is derived and studied. We develop a finite volume element approximation for one-dimensional nonlinear parabolic equations and study its existence and error analysis. Optimal error estimates in the L2-norm and HI-norm are proved. We study the two-grid method based on the finite volume element method and optimal error estimate in the Hi-norm is proved. It is shown that we can achieve asymptotically optimal approximation when the size of grids satisfies h = O（H2）. Numerical examples are presented to verify the theoretical results.