4Citations
Citations of this article
2Readers
Mendeley users who have this article in their library.
Get full text

Abstract

In [P.K. Moore, Effects of basis selection and h-refinement on error estimator reliability and solution efficiency for higher-order methods in three space dimensions, Int. J. Numer. Anal. Mod. 3 (2006) 21-51] a fixed, high-order h-refinement finite element algorithm, Href, was introduced for solving reaction-diffusion equations in three space dimensions. In this paper Href is coupled with continuation creating an automatic method for solving regularly and singularly perturbed reaction-diffusion equations. The simple quasilinear Newton solver of Moore, (2006) is replaced by the nonlinear solver NITSOL [M. Pernice, H.F. Walker, NITSOL: a Newton iterative solver for nonlinear systems, SIAM J. Sci. Comput. 19 (1998) 302-318]. Good initial guesses for the nonlinear solver are obtained using continuation in the small parameter ε{lunate}. Two strategies allow adaptive selection of ε{lunate}. The first depends on the rate of convergence of the nonlinear solver and the second implements backtracking in ε{lunate}. Finally a simple method is used to select the initial ε{lunate}. Several examples illustrate the effectiveness of the algorithm. © 2006 Elsevier Inc. All rights reserved.

Cite

CITATION STYLE

APA

Moore, P. K. (2007). Solving regularly and singularly perturbed reaction-diffusion equations in three space dimensions. Journal of Computational Physics, 224(2), 601–615. https://doi.org/10.1016/j.jcp.2006.10.015

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free