Adaptive Lagrange–Galerkin methods for unsteady convection-diffusion problems
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- by Paul Houston and Endre Süli;
- Math. Comp. 70 (2001), 77-106
- DOI: https://doi.org/10.1090/S0025-5718-00-01187-X
- Published electronically: March 3, 2000
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Abstract:
In this paper we derive an a posteriori error bound for the Lagrange–Galerkin discretisation of an unsteady (linear) convection-diffusion problem, assuming only that the underlying space-time mesh is nondegenerate. The proof of this error bound is based on strong stability estimates of an associated dual problem, together with the Galerkin orthogonality of the finite element method. Based on this a posteriori bound, we design and implement the corresponding adaptive algorithm to ensure global control of the error with respect to a user-defined tolerance.References
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Bibliographic Information
- Paul Houston
- Affiliation: Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, United Kingdom
- MR Author ID: 635107
- Email: Paul.Houston@mcs.le.ac.uk
- Endre Süli
- Affiliation: Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, United Kingdom
- Email: Endre.Suli@comlab.ox.ac.uk
- Received by editor(s): December 16, 1997
- Received by editor(s) in revised form: January 4, 1999
- Published electronically: March 3, 2000
- Additional Notes: We acknowledge the financial support of the EPSRC (Grant GR/K76221).
- © Copyright 2000 American Mathematical Society
- Journal: Math. Comp. 70 (2001), 77-106
- MSC (2000): Primary 65M15; Secondary 65M25, 65M60
- DOI: https://doi.org/10.1090/S0025-5718-00-01187-X
- MathSciNet review: 1681108