# A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations

Gabriel R. Barrenechea; Volker John; Petr Knobloch

- Volume: 47, Issue: 5, page 1335-1366
- ISSN: 0764-583X

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topBarrenechea, Gabriel R., John, Volker, and Knobloch, Petr. "A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.5 (2013): 1335-1366. <http://eudml.org/doc/273303>.

@article{Barrenechea2013,

abstract = {An extension of the local projection stabilization (LPS) finite element method for convection-diffusion-reaction equations is presented and analyzed, both in the steady-state and the transient setting. In addition to the standard LPS method, a nonlinear crosswind diffusion term is introduced that accounts for the reduction of spurious oscillations. The existence of a solution can be proved and, depending on the choice of the stabilization parameter, also its uniqueness. Error estimates are derived which are supported by numerical studies. These studies demonstrate also the reduction of the spurious oscillations.},

author = {Barrenechea, Gabriel R., John, Volker, Knobloch, Petr},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {finite element method; local projection stabilization; crosswind diffusion; convection-diffusion-reaction equation; well posedness; time dependent problem; stability; error estimates},

language = {eng},

number = {5},

pages = {1335-1366},

publisher = {EDP-Sciences},

title = {A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations},

url = {http://eudml.org/doc/273303},

volume = {47},

year = {2013},

}

TY - JOUR

AU - Barrenechea, Gabriel R.

AU - John, Volker

AU - Knobloch, Petr

TI - A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2013

PB - EDP-Sciences

VL - 47

IS - 5

SP - 1335

EP - 1366

AB - An extension of the local projection stabilization (LPS) finite element method for convection-diffusion-reaction equations is presented and analyzed, both in the steady-state and the transient setting. In addition to the standard LPS method, a nonlinear crosswind diffusion term is introduced that accounts for the reduction of spurious oscillations. The existence of a solution can be proved and, depending on the choice of the stabilization parameter, also its uniqueness. Error estimates are derived which are supported by numerical studies. These studies demonstrate also the reduction of the spurious oscillations.

LA - eng

KW - finite element method; local projection stabilization; crosswind diffusion; convection-diffusion-reaction equation; well posedness; time dependent problem; stability; error estimates

UR - http://eudml.org/doc/273303

ER -

## References

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