Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this book, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Contents Preface to the first edition page viii Preface to the second edition xi 1 Introduction… (More)
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… (More)
A cell vertex nite volume approximation of elliptic convection-dominated diiusion equations is considered in two dimensions. The scheme is shown to be stable and second-order convergent in a mesh-dependent L 2-norm.
Previous error analysis for the cell vertex scheme has been limited to situations where the cell residuals can be set to zero. However, in practical use for compressible ow computations it is necessary to extend the method by the use of distribution matrices and the careful addition of artiicial viscosity terms. In this paper we make a start on the error… (More)
Although the addition of 2nd and 4th order artiicial viscosity terms to cell vertex discretisations is standard practice, it is widely recognised that there is a lack of understanding of their exact function. This report explores the need for, and the function of, both 2nd and 4th order artiicial viscosity models, and presents improved designs.