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Numerical Study of Maximum Norm a Posteriori Error Estimates for Singularly Perturbed Parabolic Problems

  • Natalia Kopteva
  • Torsten Linß
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8236)

Abstract

A 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 two semidiscretisations in time and a full discretisation using P 1 FEM in space. Both the Backward-Euler method and the Crank-Nicolson method are considered. Certain critical details of the implementation are addressed. Based on numerical results we discuss various aspects of the error estimators in particular their effectiveness.

Keywords

a posteriori error estimate maximum norm singular perturbation elliptic reconstruction backward Euler Crank-Nicolson parabolic equation reaction-diffusion 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Natalia Kopteva
    • 1
  • Torsten Linß
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of LimerickLimerickIreland
  2. 2.Fakultät für Mathematik und InformatikFernUniversität in HagenHagenGermany

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