Premium
Optimal mesh design for the finite element approximation of reaction–diffusion problems
Author(s) -
Xenophontos Christos
Publication year - 2001
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.318
Subject(s) - polygon mesh , finite element method , reaction–diffusion system , computation , asymptotically optimal algorithm , mathematics , zero (linguistics) , range (aeronautics) , optimal design , diffusion , mathematical optimization , mathematical analysis , geometry , algorithm , physics , engineering , structural engineering , linguistics , philosophy , statistics , thermodynamics , aerospace engineering
We consider the numerical approximation of singularly perturbed problems, and in particular reaction–diffusion problems, by the h version of the finite element method. We present guidelines on how to design non‐uniform meshes both in one and two dimensions that are asymptotically optimal as the meshwidth tends to zero. We also present the results of numerical computations showing that robust, optimal rates can be achieved even in the pre‐asymptotic range. Copyright © 2001 John Wiley & Sons, Ltd.