a two-grid method for finite element solutions of nonlinear parabolic equations
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2012
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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 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.
| Reference Key |
chen2012abstracta
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|---|---|
| Authors | ;Chuanjun Chen;Wei Liu |
| Journal | science and technology of advanced materials |
| Year | 2012 |
| DOI |
10.1155/2012/391918
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