A priori diffusion-uniform error estimates for nonlinear singularly perturbed problems: BDF2, midpoint and time DG∗
Charles University in Prague, Faculty of Mathematics and Physics, Department of Numerical Mathematics, Sokolovská 83, 18675 Prague 8, Czech Republic.
Received: 10 December 2015
Revised: 19 April 2016
Accepted: 16 May 2016
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.
Mathematics Subject Classification: 65M12 / 65M15 / 65M60
Key words: Discontinuous Galerkin method / a priori error estimates / nonlinear convection-diffusion equation / diffusion-uniform error estimates
The research is supported by the Grant No. P201/13/00522S of the Czech Science Foundation. The authors are junior researchers of the University centre for mathematical modelling, applied analysis and computational mathematics (Math MAC). V. Kučera is currently a Fulbright visiting scholar at Brown University, Providence, RI, USA, supported by the J. William Fulbright Commission in the Czech Republic.
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