Geodesic
A priori diffusion-uniform error estimates for nonlinear singularly perturbed problems: BDF2, midpoint and time DG
Kučera, Václav1 ; Vlasák, Miloslav1
1 Charles University in Prague, Faculty of Mathematics and Physics, Department of Numerical Mathematics, Sokolovská 83, 18675 Prague 8, Czech Republic.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 2, pp. 537-563

Voir la notice de l'article provenant de la source Numdam

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
Keywords: 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. 
@article{M2AN_2017__51_2_537_0,
     author = {Ku\v{c}era, V\'aclav and Vlas\'ak, Miloslav},
     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},
     volume = {51},
     number = {2},
     year = {2017},
     doi = {10.1051/m2an/2016035},
     mrnumber = {3626410},
     zbl = {1372.65257},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2016035/}
}
TY  - JOUR
AU  - Kučera, Václav
AU  - Vlasák, Miloslav
TI  - A priori diffusion-uniform error estimates for nonlinear singularly perturbed problems: BDF2, midpoint and time DG
JO  - ESAIM: Mathematical Modelling and Numerical Analysis 
PY  - 2017
SP  - 537
EP  - 563
VL  - 51
IS  - 2
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2016035/
DO  - 10.1051/m2an/2016035
LA  - en
ID  - M2AN_2017__51_2_537_0
ER  - 
%0 Journal Article
%A Kučera, Václav
%A Vlasák, Miloslav
%T A priori diffusion-uniform error estimates for nonlinear singularly perturbed problems: BDF2, midpoint and time DG
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2017
%P 537-563
%V 51
%N 2
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2016035/
%R 10.1051/m2an/2016035
%G en
%F M2AN_2017__51_2_537_0
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

Cité par Sources :