Volume 6, Issue 2
Two-Grid Discretization Scheme for Nonlinear Reaction Diffusion Equation by Mixed Finite Element Methods

Luoping Chen & Yanping Chen

Adv. Appl. Math. Mech., 6 (2014), pp. 203-219.

Published online: 2014-06

Preview Full PDF 1 475
Export citation
  • Abstract

In 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 satisfy H =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.

  • Keywords

Two-grid method reaction-diffusion equations mixed finite element methods

  • AMS Subject Headings

65M12 65M15 65M60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • References
  • Hide All
    View All

@Article{AAMM-6-203, author = {Luoping Chen and Yanping Chen}, title = {Two-Grid Discretization Scheme for Nonlinear Reaction Diffusion Equation by Mixed Finite Element Methods}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2014}, volume = {6}, number = {2}, pages = {203--219}, abstract = {

In 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 satisfy H =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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.12-m12130}, url = {http://global-sci.org/intro/article_detail/aamm/14.html} }
Copy to clipboard
The citation has been copied to your clipboard