Numerical Solution of Convection-Diffusion Problems

by K. W. Morton

Accurate modelling of the interaction between convective and diffusive processes is one of the commonest challenges in the numerical approximation of partial differential equations. This is partly due to the fact that numerical algorithms, and the techniques used for their analysis, tend to be very different in the two limiting cases of elliptic and hyperbolic equations. Many different ideas and approaches have been proposed in widely differing contexts to resolve the difficulties: exponential fitting, compact differencing, upwinding, artificial viscosity, streamline diffusion, Petrov-Galerkin and evolution Galerkin being some examples from the main fields of finite difference and finite element methods. The main aim of Numerical Solution of Convection-Diffusion Problems is to draw together all these ideas and to see how they overlap and how they differ. The reader is provided with a useful and wide ranging source of algorithmic concepts and techniques of analysis. The material present