Two-Grid Method for Nonlinear Reaction-Diffusion Equations by Mixed Finite Element Methods

Authors:
Luoping Chen;Yanping Chen
Affiliations:
School of Mathematical and Computational Science, Sun Yat-Sen University, Guangzhou, P.R. China 510275;School of Mathematical Science, South China Normal University, Guangzhou, P.R. China 520631
Venue:
Journal of Scientific Computing
Year:
2011

Citing 6
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A two-grid algorithm for expanded mixed finite element approximations of semi-linear elliptic equations

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Abstract

In this paper, we investigate a scheme for nonlinear reaction-diffusion equations using the mixed finite element methods. To linearize the mixed method equations, we use the two-grid algorithm. First, we solve the original nonlinear equations on the coarse grid, then, we solve the linearized problem on the fine grid used Newton iteration once. It is shown that the algorithm can achieve asymptotically optimal approximation as long as the mesh sizes satisfy $H=\mathcal{O}(h^{\frac{1}{2}})$ . As a result, solving such a large class of nonlinear equations will not much more difficult than the solution of one linearized equation.