A priori diffusion-uniform error estimates for nonlinear singularly perturbed problems: BDF2, midpoint and time DG
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 2, pp. 537-563.

This work deals with a nonlinear nonstationary semilinear singularly perturbed convection-diffusion problem. We discretize this problem by the discontinuous Galerkin method in space and by the midpoint rule, BDF2 and quadrature variant of discontinuous Galerkin in time. We present a priori error estimates for these three schemes that are uniform with respect to the diffusion coefficient going to zero and valid even in the purely convective case.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2016035
Classification : 65M12, 65M15, 65M60
Mots clés : Discontinuous Galerkin method, a priori error estimates, nonlinear convection-diffusion equation, diffusion-uniform error estimates
Kučera, Václav 1 ; Vlasák, Miloslav 1

1 Charles University in Prague, Faculty of Mathematics and Physics, Department of Numerical Mathematics, Sokolovská 83, 18675 Prague 8, Czech Republic.
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     title = {A priori diffusion-uniform error estimates for nonlinear singularly perturbed problems: {BDF2,} midpoint and time {DG}},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {537--563},
     publisher = {EDP-Sciences},
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Kučera, Václav; Vlasák, Miloslav. A priori diffusion-uniform error estimates for nonlinear singularly perturbed problems: BDF2, midpoint and time DG. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 2, pp. 537-563. doi : 10.1051/m2an/2016035. http://www.numdam.org./articles/10.1051/m2an/2016035/

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