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.
Accepté le :
DOI : 10.1051/m2an/2016035
Keywords: Discontinuous Galerkin method, a priori error estimates, nonlinear convection-diffusion equation, diffusion-uniform error estimates
Kučera, Václav 1 ; Vlasák, Miloslav 1
@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},
year = {2017},
publisher = {EDP Sciences},
volume = {51},
number = {2},
doi = {10.1051/m2an/2016035},
mrnumber = {3626410},
zbl = {1372.65257},
language = {en},
url = {https://www.numdam.org/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 - https://www.numdam.org/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 https://www.numdam.org/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
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