Journal of Scientific Computing

, Volume 49, Issue 3, pp 383–401

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

Article

DOI: 10.1007/s10915-011-9469-3

Cite this article as:
Chen, L. & Chen, Y. J Sci Comput (2011) 49: 383. doi:10.1007/s10915-011-9469-3

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.

Keywords

Two-grid method Reaction-diffusion equations Mixed finite element methods 

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.School of Mathematical and Computational ScienceSun Yat-Sen UniversityGuangzhouP.R. China
  2. 2.School of Mathematical ScienceSouth China Normal UniversityGuangzhouP.R. China

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