Multiscale Finite Element Formulation for the 3D Diffusion-Convection Equation

Abstract

In this work we present a numerical study of the Dynamic Diffusion (DD) method for solving diffusion-convection problems with dominant convection on three dimensional domains. The DD method is a two-scale nonlinear model for convection-dominated transport problems, obtained by incorporating to the multiscale formulation a nonlinear dissipative operator acting isotropically in both scales of the discretization. The standard finite element spaces are enriched with bubble functions in order to add stability properties to the numerical model. The DD method for two dimensional problems results in good solutions compared to other known methods. We analyze the impact of this methodology on three dimensional domains comparing its numerical results with those obtained using the Consistent Approximate Upwind (CAU) method.