Geodesic
A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 5, pp. 1335-1366

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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.

DOI : 10.1051/m2an/2013071
Classification : 65N30, 65N12, 65N15, 65M60
Keywords: finite element method, local projection stabilization, crosswind diffusion, convection-diffusion-reaction equation, well posedness, time dependent problem, stability, error estimates 
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     author = {Barrenechea, Gabriel R. and John, Volker and Knobloch, Petr},
     title = {A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1335--1366},
     publisher = {EDP-Sciences},
     volume = {47},
     number = {5},
     year = {2013},
     doi = {10.1051/m2an/2013071},
     mrnumber = {3100766},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013071/}
}
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Barrenechea, Gabriel R.; John, Volker; Knobloch, Petr. A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 5, pp. 1335-1366. doi: 10.1051/m2an/2013071

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