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Zbl 1062.65104
Chen, Yanping; Huang, Yunqing; Yu, Dehao
A two-grid method for expanded mixed finite-element solution of semilinear reaction-diffusion equations. (English)
[J] Int. J. Numer. Methods Eng. 57, No. 2, 193-209 (2003). ISSN 0029-5981

Summary: We present a scheme for solving two-dimensional semilinear reaction-diffusion equations using an expanded mixed finite element method. To linearize the mixed-method equations, we use a two-grid algorithm based on the Newton iteration method. The solution of a non-linear system on the fine space is reduced to the solution of two small (one linear and one non-linear) systems on the coarse space and a linear system on the fine space. It is shown that the coarse grid can be much coarser than the fine grid and achieve asymptotically optimal approximation as long as the mesh sizes satisfy $H=O(h^{1/3})$. As a result, solving such a large class of non-linear equation will not be much more difficult than solving one single linearized equation.

MSC 2000:: *65M60 Finite numerical methods (IVP of PDE)
35K57 Reaction-diffusion equations

Keywords: reaction-diffusion equations; expanded mixed finite elements; two-grid methods

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Zentralblatt MATH Berlin [Germany]