Evolution-Galerkin methods and their supraconvergence

Summary.

Evolution-Galerkin methods for partial differential equations of the form$u_t +L(u)=0$ are characterised by (i) the use of some form of approximation to the corresponding evolution operator $E(t)$, and (ii) projection onto an approximation space $S_h$ to obtain $\{U^n\}$. In this paper we concentrate on characteristic-Galerkin and Lagrange-Galerkin methods to derive basic error estimates for multidimensional convection problems. Methods covered include those using recovery techniques to improve accuracy. Many schemes exhibit a supraconvergence phenomenon and a general technique for its analysis is given, together with a number of particular examples.