Evolution Galerkin methods for hyperbolic systems in two space dimensions

Authors:
M. Lukácová-Medvid'ová, K. W. Morton and G. Warnecke

Journal:
Math. Comp. **69** (2000), 1355-1384

MSC (1991):
Primary 35L05, 65M06; Secondary 35L45, 35L65, 65M25, 65M15

DOI:
https://doi.org/10.1090/S0025-5718-00-01228-X

Published electronically:
February 23, 2000

MathSciNet review:
1709154

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Abstract | References | Similar Articles | Additional Information

The subject of the paper is the analysis of three new evolution Galerkin schemes for a system of hyperbolic equations, and particularly for the wave equation system. The aim is to construct methods which take into account all of the infinitely many directions of propagation of bicharacteristics. The main idea of the evolution Galerkin methods is the following: the initial function is evolved using the characteristic cone and then projected onto a finite element space. A numerical comparison is given of the new methods with already existing methods, both those based on the use of bicharacteristics as well as commonly used finite difference and finite volume methods. We discuss the stability properties of the schemes and derive error estimates.

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Additional Information

**M. Lukácová-Medvid'ová**

Affiliation:
Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany

Address at time of publication:
Department of Mathematics, Faculty of Mechanical Engineering, Technical University Brno, Technická 2, 61639 Brno, Czech Republic

Email:
Lukacova@fme.vutbr.cz

**K. W. Morton**

Affiliation:
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, United Kingdom (also Oxford University Computing Laboratory)

Email:
Bill.Morton@comlab.ox.ac.uk

**G. Warnecke**

Affiliation:
Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany

Email:
Gerald.Warnecke@mathematik.uni-magdeburg.de

DOI:
https://doi.org/10.1090/S0025-5718-00-01228-X

Keywords:
Genuinely multidimensional schemes,
hyperbolic systems,
wave equation,
Euler equations,
evolution Galerkin schemes

Received by editor(s):
January 2, 1998

Received by editor(s) in revised form:
January 4, 1999

Published electronically:
February 23, 2000

Article copyright:
© Copyright 2000
American Mathematical Society