Robust A Posteriori Error Estimates for Nonstationary Convection-Diffusion Equations

Authors:
R. Verfürth
Affiliations:
-
Venue:
SIAM Journal on Numerical Analysis
Year:
2005

Citing 0
Cited 6

Parallel finite element computations of three-dimensional flow problems using padfem2

International Journal of Parallel, Emergent and Distributed Systems
An adaptive algorithm for the Crank-Nicolson scheme applied to a time-dependent convection-diffusion problem

Journal of Computational and Applied Mathematics
A posteriori error analysis of time-dependent Stokes problem by Chorin-Temam scheme

Calcolo: a quarterly on numerical analysis and theory of computation
Reliable and efficient a posteriori error estimates for finite element approximations of the parabolic p-Laplacian

Calcolo: a quarterly on numerical analysis and theory of computation
On Adaptive Eulerian---Lagrangian Method for Linear Convection---Diffusion Problems

Journal of Scientific Computing
An a posteriori error estimator for an unsteady advection-diffusion-reaction problem

Computers & Mathematics with Applications

Quantified Score

Hi-index	0.01

Visualization

Abstract

We consider discretizations of convection dominated nonstationary convection-diffusion equations by A-stable $\theta$-schemes in time and conforming finite elements in space on locally refined, isotropic meshes. For these discretizations we derive a residual a posteriori error estimator. The estimator yields upper bounds on the error which are global in space and time and lower bounds that are global in space and local in time. The error estimates are fully robust in the sense that the ratio between upper and lower bounds is uniformly bounded in time, does not depend on any step-size in space or time nor on any relation between these both, and is uniformly bounded with respect to the size of the convection. Moreover, the estimates are uniform with respect to the size of the zero-order reaction term and also hold for the limit case of vanishing reaction.