A second order scheme for a time-dependent, singularly perturbed convection-diffusion equation

Authors:
Wim Lenferink
Affiliations:
Department of Mathematics, Linköping University, S-58183 Linköping, Sweden
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

Citing 4
Cited 0

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Pointwise convergence of approximations to a convection—diffusion equation on a Shishkin mesh

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Abstract

We consider a numerical scheme for a one-dimensional, time-dependent, singularly perturbed convection-diffusion problem. The problem is discretized in space by a standard finite element method on a Bakhvalov-Shishkin type mesh. The space error is measured in an L2 norm. For the time integration, the implicit midpoint rule is used. The fully discrete scheme is shown to be convergent of order 2 in space and time, uniformly in the singular perturbation parameter.