## Abstract and Applied Analysis

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

#### Abstract

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 ${H}^{1}$-norm $O(h+{H}^{2})$ 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 $h=O({H}^{2})$.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 803615, 6 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412279742

Digital Object Identifier
doi:10.1155/2014/803615

Mathematical Reviews number (MathSciNet)
MR3178890

#### Citation

Chen, Chuanjun; Liu, Wei; Zhao, Xin. A Two-Grid Finite Element Method for a Second-Order Nonlinear Hyperbolic Equation. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 803615, 6 pages. doi:10.1155/2014/803615. https://projecteuclid.org/euclid.aaa/1412279742

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