一维非线性抛物问题两层网格有限体积元逼近

Abstract

Abstract: 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 H¹-norm are proved. We study the two-grid method based on the finite volume element method and optimal error estimate in the H¹-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.

Key words: Finite volume element method, Two-grid, Nonlinear, Parabolic equation, Error estimate

CLC Number:

O241.82

Chen Chuanjun, Zhang Xiaoyan, Zhao Xin. A Two-Grid Finite Volume Element Approximation for One-Dimensional Nonlinear Parabolic Equations[J].Acta mathematica scientia,Series A, 2017, 37(5): 962-975.

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

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