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Maximum Norm a Posteriori Error Estimation For a Time-dependent Reaction-diffusion Problem
-
Natalia Kopteva
and
Torsten Linß
Published/Copyright:
January 1, 2012
Abstract
A semilinear second-order singularly perturbed parabolic equation in one space dimension is considered. For this equation, we give computable a posteriori error estimates in the maximum norm for a difference scheme that uses Backward-Euler in time and central differencing in space. Sharp L¹-norm bounds for the Green's function of the parabolic operator and its derivatives are derived that form the basis of the a posteriori error analysis. Numerical results are presented.
Keywords: a posteriori error estimate; maximum norm; singular perturbation; Backward-Euler; parabolic equations; reaction-diffusion
Received: 2011-12-19
Revised: 2012-03-05
Accepted: 2012-03-20
Published Online: 2012
Published in Print: 2012
© Institute of Mathematics, NAS of Belarus
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Keywords for this article
a posteriori error estimate;
maximum norm;
singular perturbation;
Backward-Euler;
parabolic equations;
reaction-diffusion
Articles in the same Issue
- Martin Stynes – 60
- Divergence Preserving Interpolation on Anisotropic Quadrilateral Meshes
- Numerical Experiments for a Singularly Perturbed Parabolic Problem with Degenerating Convective Term and Discontinuous Source
- A Note on the Convergence Analysis of a Diffuse-domain Approach
- A Finite Element Method for a Noncoercive Elliptic Problem with Neumann Boundary Conditions
- A Localized Maximum Principle
- Maximum Norm a Posteriori Error Estimation For a Time-dependent Reaction-diffusion Problem
- A Singularly Perturbed Convection Diffusion Turning Point Problem with an Interior Layer
- A Local Projection Stabilization Method with Shock Capturing and Diagonal Mass Matrix for Solving Non-stationary Transport Dominated Problems
