Error estimates for a nonlinear local projection stabilization of transient convection--diffusion--reaction equations

Petr  Knobloch

doi:10.3934/dcdss.2015.8.901

Article Contents

2015, Volume 8, Issue 5: 901-911. Doi: 10.3934/dcdss.2015.8.901

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Error estimates for a nonlinear local projection stabilization of transient convection--diffusion--reaction equations

Petr Knobloch^1,

1.
Department of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 18675 Praha 8

Received: January 31, 2014

Revised: July 31, 2014

Published: October 2015

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Abstract

A recently proposed local projection stabilization (LPS) finite element method containing a nonlinear crosswind diffusion term is analyzed for a transient convection-diffusion-reaction equation using a one-step $\theta$-scheme as temporal discretization. Both the fully nonlinear method and its semi-implicit variant are considered. Solvability of the discrete problem is established and a priori error estimates in the LPS norm are proved. Uniqueness of the discrete solution is proved for the semi-implicit approach or for sufficiently small time steps.

Keywords:

Finite element method,
local projection stabilization,
crosswind diffusion,
transient convection-diffusion-reaction equation,
well posedness,
error estimates.

Mathematics Subject Classification: 65M60, 65M12, 65M15.

Citation:

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References

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