PETROV—GALERKIN METHODS ON ISOPARAMETRIC BILINEAR AND BIQUADRATIC ELEMENTS TESTED FOR A SCALAR CONVECTION—DIFFUSION PROBLEM

Abstract

A number of finite element formulations involving discontinuous weighting functions have been tested against analytic solutions for a steady scalar convection—diffusion problem at intermediate Peclet number, with a ‘hard’ downstream boundary condition. The emphasis is on extending these methods to isoparametric bilinear and biquadratic elements. In order to do this a procedure is given for the exact calculation of shape function Laplacians. Having confirmed the success of the Brooks—Hughes streamline upwind Petrov—Galerkin (SUPG) method for isoparametric bilinear elements, formulations for biquadratic elements are examined. Galerkin least squares offers little advantage over SUPG in the test problem. The generalized Galerkin method of Donea et al. gave excellent results, but because of concern over the possibility of cross‐streamline artificial diffusion in some cases, a strictly streamline formulation incorporating the optimal parameters of Donea et al. is proposed. This gave excellent results on a sufficiently refined mesh.

Citation

PETERA, J., NASSEHI, V. and PITTMAN, J.F.T. (1993), "PETROV—GALERKIN METHODS ON ISOPARAMETRIC BILINEAR AND BIQUADRATIC ELEMENTS TESTED FOR A SCALAR CONVECTION—DIFFUSION PROBLEM", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 3 No. 3, pp. 205-221. https://doi.org/10.1108/eb017526