Analysis of finite element schemes for convection‐type problems

Abstract

Abstract Various finite element schemes of the Bubnov–Galerkin and Taylor–Galerkin types are analysed to obtain the expressions of truncation errors. This way, dispersion errors in the transient, and diffusion errors both in the transient and in the steady state, are identified. Then, with reference to the transient advection–diffusion equation, stability limits are determined by means of a general von Neumann procedure. Finally, the operational equivalence between Taylor–Galerkin methods, utilized for pseudo‐transient calculations, and Petrov–Galerkin methods, derived for the steady state forms of the advection–diffusion equation, is illustrated. Theoretical conclusions are supported by the results of numerical experiments.