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

Chuanjun Chen and Wei Liu

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

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.

Date: 2012
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https://doi.org/10.1155/2012/391918

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:391918

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