| Institution: | Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany ; Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, United Kingdom (also Oxford University Computing Laboratory) ; Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany |
| Abstract: | 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. |
