A Two-Grid Method for Finite Element Solutions of Nonlinear Parabolic Equations

Abstract EN

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 H.

The nonlinearities are expanded about the coarse grid solution on a fine gird of size h, and the resulting linear system is solved on the fine grid.

A priori error estimates are derived with the H1-norm O(h+H2) which shows that the two-grid method achieves asymptotically optimal approximation as long as the mesh sizes satisfy h=O(H2).

An example is also given to illustrate the theoretical results.