Volume 9, Issue 3
A New Two-Grid Method for Expanded Mixed Finite Element Solution of Nonlinear Reaction Diffusion Equations

Shang Liu & Yanping Chen

Adv. Appl. Math. Mech., 9 (2017), pp. 757-774.

Published online: 2018-05

Preview Purchase PDF 2 891
Export citation
  • Abstract

In the paper, we present an efficient two-grid method for the approximation of two-dimensional nonlinear reaction-diffusion equations using a expanded mixed finite-element method. We transfer the nonlinear reaction diffusion equation into first order nonlinear equations. The solution of the nonlinear system on the fine space is reduced to the solutions of two small (one linear and one non-linear) systems on the coarse space and a linear system on the fine space. Moreover, we obtain the error estimation for the two-grid algorithm. It is showed that coarse space can be extremely coarse and achieve asymptotically optimal approximation as long as the mesh sizes satisfy h k+1=O(H3k+1 )

  • Keywords

Error estimation, mixed finite elements, reaction-diffusion equations, two-grid methods.

  • AMS Subject Headings

65N30, 65N15, 65M12

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
Copy to clipboard
The citation has been copied to your clipboard