Mixed finite element methods for a fourth order reaction diffusion equation

2011 ◽  
Vol 28 (4) ◽  
pp. 1227-1251 ◽  
Author(s):  
P. Danumjaya ◽  
Amiya K. Pani
Keyword(s):  
Finite Element ◽  
Diffusion Equation ◽  
Fourth Order ◽  
Finite Element Methods ◽  
Mixed Finite Element ◽  
Reaction Diffusion ◽  
Order Reaction ◽  
Mixed Finite Element Methods ◽  
Reaction Diffusion Equation

Two-Grid Discretization Scheme for Nonlinear Reaction Diffusion Equation by Mixed Finite Element Methods

2014 ◽  
Vol 6 (2) ◽  
pp. 203-219 ◽  
Author(s):  
Luoping Chen ◽  
Yanping Chen
Keyword(s):  
Finite Element ◽  
Nonlinear Equations ◽  
Finite Element Methods ◽  
Mixed Finite Element ◽  
Reaction Diffusion ◽  
Mixed Finite Element Methods ◽  
Reaction Diffusion Equations ◽  
Reaction Diffusion Equation ◽  
Fine Mesh ◽  
Nonlinear Reaction

AbstractIn this paper, we study an efficient scheme for nonlinear reaction-diffusion equations discretized by mixed finite element methods. We mainly concern the case when pressure coefficients and source terms are nonlinear. To linearize the nonlinear mixed equations, we use the two-grid algorithm. We first solve the nonlinear equations on the coarse grid, then, on the fine mesh, we solve a linearized problem using Newton iteration once. It is shown that the algorithm can achieve asymptotically optimal approximation as long as the mesh sizes satisfyH=O(h1/2). As a result, solving such a large class of nonlinear equations will not be much more difficult than getting solutions of one linearized system.

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