STABILIZED FINITE-ELEMENT METHODS FOR STEADY ADVECTION-DIFFUSION WITHPRODUCTION

Finite element methods for solving equations of steady advection-diffu sion with production are constructed, employing a linear source to mod el production. The Galerkin method requires relatively fine meshes to retain an acceptable degree of accuracy for wide ranges of values of t he physical coefficients. Numerous criteria for improved accuracy via Galerkin/least-squares are proposed and examined in the entire paramet er space. Of these, several provide the lowest error in nodal amplific ation factors, each in a certain range of ratios of physical coefficie nts. Guidelines for required mesh resolutions are presented for Galerk in and Galerkin/least-squares, showing that in large parts of the para meter space substantial savings may be obtained by employing Galerkin/ least-squares. Galerkin/least-squares/gradient least-squares, a new va riation of the Galerkin method, is designed to provide exact nodal amp lification factors, offering accurate solutions at any resolution. Num erical tests validate these conclusions.