Abstract

GARZON, DIEGO; GALEANO, CARLOS  and  MANTILLA, JUAN. SPACE-TIME STABILITY ANALYSIS OF THE STREAMLINE UPWIND PETROV-GALERKIN METHOD FOR DIFUSSION-ADVECTION EQUATIONS. Dyna rev.fac.nac.minas [online]. 2010, vol.77, n.162, pp.359-369. ISSN 0012-7353.

This article analyzes the space and temporal stability of a numerical solution of the diffusion-advection equation through the streamline upwind Petrov-Galerkin Method (SUPG), along with a Backward-Euler temporal discretization. In the first part the fundamental concepts of the SUPG technique for space stabilization in two dimensions, and the temporal discretization considerations are presented. Next the methodology and necessary expressions for computer implementation of the method are treated. Two cases of study are developed in which the space and temporal stability of the implemented solution are compared with those obtained by means of the conventional Bubnov-Galerkin approach. The error in the energy norm is used to analyze the stability of the obtained results. Videos and additional graphs of the problems in this article can be downloaded from www.gnum.unal.edu.co.

Keywords : Petrov-Galerkin; Backward-Euler; Stabilization; Diffusion; Advection.

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