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A unified framework for time-dependent singularly perturbed problems with discontinuous Galerkin methods in time


Authors: Sebastian Franz and Gunar Matthies
Journal: Math. Comp. 87 (2018), 2113-2132
MSC (2010): Primary 65M12, 65M15, 65M60
DOI: https://doi.org/10.1090/mcom/3326
Published electronically: January 23, 2018
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Abstract: In this paper we present a unified framework for the error analysis of time-dependent singularly perturbed problems with discontinuous Galerkin time discretisation. Its general analysis relies on spatial error estimates known from stationary problems and the properties of the discontinuous Galerkin time discretisation.

We present also applications of our framework to second- and fourth-order singularly perturbed problems in estimation and simulation.


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Additional Information

Sebastian Franz
Affiliation: Institute of Scientific Computing, Technische Universität Dresden, 01062 Dresden, Germany
Email: sebastian.franz@tu-dresden.de

Gunar Matthies
Affiliation: Institute of Numerical Mathematics, Technische Universität Dresden, 01062 Dresden, Germany
Email: gunar.matthies@tu-dresden.de

DOI: https://doi.org/10.1090/mcom/3326
Received by editor(s): January 25, 2016
Received by editor(s) in revised form: December 6, 2016, and March 22, 2017
Published electronically: January 23, 2018
Article copyright: © Copyright 2018 American Mathematical Society

American Mathematical Society