✦ LIBER ✦

Implicit interpolation error-based error estimation for reaction-diffusion equations in two space dimensions

✍ Scribed by Peter K. Moore

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 230 KB
Volume: 192
Category: Article
ISSN: 0045-7825
DOI: 10.1016/s0045-7825(03)00420-1

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✦ Synopsis

Several authors have proposed an error estimation strategy for the finite element method applied to linear reactiondiffusion equations in two space dimensions based on an odd/even-order dichotomy principle. For odd-order approximations the estimates are computed directly. For even-order approximations a second solution is computed. Although both estimators are asymptotically exact the latter are more robust than the former. Herein the even-order method is extended to all orders greater than one, thereby recovering robustness for odd orders. Proofs of asymptotic exactness are extended to nonlinear reaction-diffusion equations. Computational results demonstrating their effectiveness are presented.

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