A two-grid method for finite volume element approximations of second-order nonlinear hyperbolic equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:233

Article

Chen, Chuanjun¹  Liu, Wei² 

[1] Yantai Univ, Dept Math & Informat Sci, Yantai 264005, Peoples R China

[2] Shandong Econ Univ, Sch Math & Stat, Jinan 250014, Peoples R China

关键词: Two-grid method;    Second-order hyperbolic;    Finite volume element method;    Error estimates;   

DOI  :  10.1016/j.cam.2009.11.043

来源: Elsevier

【 摘 要 】

The two-grid method is studied for solving a two-dimensional second-order nonlinear hyperbolic equation using finite volume element method. The method is based on two different finite element spaces defined on one coarse grid with grid size H and one fine grid with grid size h, respectively. The nonsymmetric and nonlinear iterations are only executed on the coarse grid and the fine grid solution can be obtained in a single symmetric and linear step. It is proved that the coarse grid can be much coarser than the fine grid. A prior error estimate in the H-1-norm is proved to be O(h+H-3 vertical bar In H vertical bar) for the two-grid semidiscrete finite volume element method. With these proposed techniques, solving such a large class of second-order nonlinear hyperbolic equations will not be much more difficult than solving one single linearized equation. Finally, a numerical example is presented to validate the usefulness and efficiency of the method. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

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