GFEM AND LSFEM IN THE SOLUTION OF THE TRANSIENT BIDIMENSIONAL CONVECTION-DIFFUSION EQUATION

Abstract

Convection dominated flows result in a hyperbolic system of equations which leads to ill-conditioned matrices and oscillatory approximations when using the classical Galerkin Finite Element Method (GFEM). In this paper, the Least Square Finite Method (LSFEM) is introduced in the study of transient bidimensional convection-diffusion problems. The differentiated equation of second order which describes the convective-diffusive phenomenon is transformed into an equivalent system of partial differentiated equations of first order which is discretized by the formulation of the LSFEM resulting in a defined algebraic, symmetrical and positive system. The performance of the method is verified by the solution of a test- problem.