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Lagrangian and moving mesh methods for the convection diffusion equation. (English) Zbl 1136.65089
The authors present a semi Lagrangian method for the convection-diffusion equation. Error estimates for both semi and fully discrete finite element approximations are provided for convection dominated flows. The estimates are posed in terms of projections and the dependence of various constants upon the diffusion parameter is characterized. Error estimates independent of the diffusion constant are also obtained when the velocity field is computed exactly.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
76R10 Free convection
76R50 Diffusion
76M10 Finite element methods applied to problems in fluid mechanics
35K15 Initial value problems for second-order parabolic equations
Software:
NKA
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References:
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