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.
Chuanjun Chen. Wei Liu. "A Two-Grid Method for Finite Element Solutions of Nonlinear Parabolic Equations." Abstr. Appl. Anal. 2012 (SI06) 1 - 11, 2012. https://doi.org/10.1155/2012/391918