ANALYSIS OF FINITE-ELEMENT SCHEMES FOR CONVECTION-TYPE PROBLEMS

Various finite element schemes of the Bubnov-Galerkin and Taylor-Galer kin types are analysed to obtain the expressions of truncation errors. This way, dispersion errors in the transient, and diffusion errors bo th in the transient and in the steady state, are identified. Then, wit h reference to the transient advection-diffusion equation, stability l imits are determined by means of a general von Neumann procedure. Fina lly, the operational equivalence between Taylor-Galerkin methods, util ized for pseudo-transient calculations, and Petrov-Galerkin methods, d erived for the steady state forms of the advection-diffusion equation, is illustrated. Theoretical conclusions are supported by the results of numerical experiments.