一类非线性对流扩散方程两重网格特征有限元方法及误差估计

Abstract

Abstract:

A two-grid characteristic finite element approximation is presented and discussed for nonlinear convection-diffusion equations. Piecewise linear trial functions are used to develop the finite element scheme. In this two-grid scheme, the full nonlinear problem is solved only on a coarse grid with grid size H. The nonlinearities are expanded by one Newton-like iteration about the coarse grid solution on a fine gird of size h. The resulting linear system is solved only on the fine grid. A prior error estimates are derived with the L²-norm O(?t +h²+H^4-d/2), where d≥1 is the spacial dimension.

Key words: Two-grid, Finite element method, Nonlinear, Error estimates

CLC Number:

65N12

CHEN Chuan-Jun, ZHAO Xin. Analysis of a Two-grid Method for Characteristic Finite Element Solutions of Nonlinear Convection-diffusion Equations[J].Acta mathematica scientia,Series A, 2014, 34(3): 643-654.

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Analysis of a Two-grid Method for Characteristic Finite Element Solutions of Nonlinear Convection-diffusion Equations

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