The Mathematical Institute, University of Oxford, Eprints Archive

Adaptive Lagrange-Galerkin methods for unsteady convection-dominated diffusion problems

Houston, P. and Suli, Endre (1995) Adaptive Lagrange-Galerkin methods for unsteady convection-dominated diffusion problems. Technical Report. Unspecified. (Submitted)



In this paper we derive an a posteriori error estimate in the L²(L²) norm for the Lagrange-Galerkin discretisation of the unsteady two-dimensional convection-diffusion problem. The proof of the error estimate is based on so-called strong stability estimates of an associated backward dual problem, together with the Galerkin orthogonality of the finite element method. Based on this a posteriori error estimate, we design an adaptive algorithm for determining both the space and time discretisation parameters in such a way as to yield global error control in the L²(L²) norm with respect to a pre-determined tolerance. Moreover, the reliability and efficiency of this adaptive strategy are numerically verified on test problems with known analytic solutions.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1333
Deposited By: Lotti Ekert
Deposited On:12 Jun 2011 08:53
Last Modified:29 May 2015 19:01

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