Numerical approximation of solution derivatives of singularly perturbed parabolic problems of convection-diffusion type
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- by J. L. Gracia and E. O’Riordan PDF
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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.References
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Additional Information
- J. L. Gracia
- Affiliation: IUMA - Department of Applied Mathematics, University of Zaragoza, 50018 Zaragoza, Spain
- Email: jlgracia@unizar.es
- E. O’Riordan
- Affiliation: School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland
- Email: eugene.oriordan@dcu.ie
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Math. Comp. 85 (2016), 581-599
- MSC (2010): Primary 65M15, 65M12
- DOI: https://doi.org/10.1090/mcom/2998
- MathSciNet review: 3434872