Stabilized finite element methods for steady advection-diffusion with production

Finite element methods for solving equations of steady advection-diffusion with production are constructed, employing a linear source to model production. The Galerkin method requires relatively fine meshes to retain an acceptable degree of accuracy for wide ranges of values of the physical coefficients. Numerous criteria for improved accuracy via Galerkin/least-squares are proposed and examined in the entire parameter space. Of these, several provide the lowest error in nodal amplification factors, each in a certain range of ratios of physical coefficients. Guidelines for required mesh resolutions are presented for Galerkin and Galerkin/least-squares, showing that in large parts of the parameter space substantial savings may be obtained by employing Galerkin/least-squares. Galerkin/least-squares/gradient least-squares, a new variation of the Galerkin method, is designed to provide exact nodal amplification factors, offering accurate solutions at any resolution. Numerical tests validate these conclusions.