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

Franz, Sebastian; Matthies, Gunar

doi:10.1090/mcom/3326

A unified framework for time-dependent singularly perturbed problems with discontinuous Galerkin methods in time
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by Sebastian Franz and Gunar Matthies PDF

Math. Comp. 87 (2018), 2113-2132 Request permission

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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