A priori diffusion-uniform error estimates for nonlinear singularly perturbed problems: BDF2, midpoint and time DG

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 est...

Full description

Saved in:
Bibliographic Details
Published in:ESAIM. Mathematical modelling and numerical analysis 2017-03, Vol.51 (2), p.537-563
Main Authors: Kučera, Václav, Vlasák, Miloslav
Format: Article
Language:English
Subjects:
65M12
65M15
65M60
a priori error estimates
Convection-diffusion equation
Diffusion
Diffusion coefficient
diffusion-uniform error estimates
Discontinuous Galerkin method
Galerkin method
nonlinear convection-diffusion equation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0764-583X
1290-3841
DOI:10.1051/m2an/2016035