Implicit-explicit time stepping with spatial discontinuous finite elements

Authors:
Willem Hundsdorfer;Jérôme Jaffré
Affiliations:
CWI, P.O. Box 94079, 1090 GB Amsterdam, Netherlands;INRIA-Rocquencourt, BP 105, 789153 Le Chesnay cédex, France
Venue:
Applied Numerical Mathematics
Year:
2003

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Abstract

In this paper a combination of discontinuous, piecewise linear, finite elements with BDF2 implicit-explicit time stepping is considered for convection-reaction equations. Combined with low order quadrature rules, this leads to convenient schemes. We shall consider the effect of such low order quadrature rules on accuracy and stability for one-dimensional problems. Furthermore, attention will be given to the stability and TVD properties of the explicit BDF2-type formula used for convection in the implicit-explicit time stepping.