Copyright © 2012 Chuanjun Chen and Wei Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A two-grid method is presented and discussed for a finite element approximation to a nonlinear parabolic equation in two space dimensions. Piecewise linear trial functions are used. In this two-grid scheme, the full nonlinear problem is solved only on a coarse grid with grid size . The nonlinearities are expanded about the coarse grid solution on a fine gird of size , and the resulting linear system is solved on the fine grid. A priori error estimates are derived with the -norm which shows that the two-grid method achieves asymptotically optimal approximation as long as the mesh sizes satisfy . An example is also given to illustrate the theoretical results.