Solving regularly and singularly perturbed reaction-diffusion equations in three space dimensions

✍ Scribed by Peter K. Moore

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 680 KB
• Volume: 224
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1016/j.jcp.2006.10.015

✦ Synopsis

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 . Two strategies allow adaptive selection of . The first depends on the rate of convergence of the nonlinear solver and the second implements backtracking in . Finally a simple method is used to select the initial . Several examples illustrate the effectiveness of the algorithm.