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Uniform approximation of singularly perturbed reaction‐diffusion problems by the finite element method on a Shishkin mesh
Author(s) -
Xenophontos Christos,
Fulton Scott R.
Publication year - 2003
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.10034
Subject(s) - mathematics , piecewise , finite element method , singular perturbation , polygon mesh , computation , partial differential equation , mathematical analysis , boundary value problem , reaction–diffusion system , numerical analysis , boundary (topology) , geometry , algorithm , physics , thermodynamics
We consider the numerical approximation of singularly perturbed reaction‐diffusion problems over two‐dimensional domains with smooth boundary. Using the h version of the finite element method over appropriately designed piecewise uniform (Shishkin) meshes, we are able to uniformly approximate the solution at a quasi‐optimal rate. The results of numerical computations showing agreement with the analysis are also presented. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 89–111, 2003