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A second-order scheme for singularly perturbed differential equations with discontinuous source term
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H.-G. Roos
Published/Copyright:
November 15, 2010
Abstract
A Galerkin finite element method that uses piecewise linear functions on Shishkin- and Bakhvalov–Shishkin-type of meshes is applied to a linear reaction-diffusion equation with discontinuous source term. The method is shown to be convergent, uniformly in the perturbation parameter, of order N–2 ln2N for the Shishkin-type mesh and N–2 for the Bakhvalov–Shishkin-type mesh, where N is the mesh size number. Numerical experiments support our theoretical results.
Received: 2001-05-30
Revised: 2002-07-01
Published Online: 2010-11-15
Published in Print: 2002-December
© VSP 2002
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Keywords for this article
Reaction-diffusion problems;
singular perturbation;
finite element method;
Shishkin mesh
