Evolution-Galerkin methods and their supraconvergence

Summary. Evolution-Galerkin methods for partial differential equations of the form are characterised by (i) the use of some form of approximation to the corresponding evolution operator , and (ii) projection onto an approximation space to obtain . 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. Received July 5, 1993 / Revised version received February 6, 1995