A Two-Grid Finite Element Method for a Second-Order Nonlinear Hyperbolic Equation

We present a two-grid finite element scheme for the approximation of a second-order nonlinear hyperbolic equation in two space dimensions. In the two-grid scheme, the full nonlinear problem is solved only on a coarse grid of size H. The nonlinearities are expanded about the coarse grid solution on t...

Full description

Saved in:
Bibliographic Details
Main Authors: Chuanjun Chen, Wei Liu, Xin Zhao
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/803615
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We present a two-grid finite element scheme for the approximation of a second-order nonlinear hyperbolic equation in two space dimensions. In the two-grid scheme, the full nonlinear problem is solved only on a coarse grid of size H. The nonlinearities are expanded about the coarse grid solution on the fine gird of size h. The resulting linear system is solved on the fine grid. Some a priori error estimates are derived with the H1-norm O(h+H2) for the two-grid finite element method. Compared with the standard finite element method, the two-grid method achieves asymptotically same order as long as the mesh sizes satisfy h=O(H2).
ISSN:1085-3375
1687-0409