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Numerical approximation of solution derivatives of singularly perturbed parabolic problems of convection-diffusion type

Authors: J. L. Gracia and E. O’Riordan
Journal: Math. Comp. 85 (2016), 581-599
MSC (2010): Primary 65M15, 65M12
Published electronically: July 13, 2015
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Abstract: Numerical approximations to the solution of a linear singularly perturbed parabolic convection-diffusion problem are generated using a backward Euler method in time and an upwinded finite difference operator in space on a piecewise-uniform Shishkin mesh. A proof is given to show first order convergence of these numerical approximations in an appropriately weighted $ C^1$-norm. Numerical results are given to illustrate the theoretical error bounds.

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Additional Information

J. L. Gracia
Affiliation: IUMA - Department of Applied Mathematics, University of Zaragoza, 50018 Zaragoza, Spain

E. O’Riordan
Affiliation: School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland

Keywords: Singular perturbation, approximation of derivatives, convection-diffusion problem, Shishkin mesh
Received by editor(s): February 19, 2013
Received by editor(s) in revised form: September 24, 2014
Published electronically: July 13, 2015
Additional Notes: The second author is the corresponding author
Article copyright: © Copyright 2015 American Mathematical Society