Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 49, Issue 3, Pages 383-401Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-011-9469-3
Keywords
Two-grid method; Reaction-diffusion equations; Mixed finite element methods
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Funding
- Foundation for Talent Introduction of Guangdong Provincial University
- Guangdong Province Universities and Colleges
- National Science Foundation of China [10971074]
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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=O(h(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.
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