A multiscale finite element method for the solution of transport equations

Authors:
M. Parvazinia
Affiliations:
Iran Polymer and Petrochemical Institute, P.O. Box 14965-115, Tehran, Iran
Venue:
Finite Elements in Analysis and Design
Year:
2011

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Abstract

A multiscale Galerkin finite element scheme based on the residual free bubble function method is proposed to generate stable and accurate solutions for the transport equations namely diffusion-reaction (DR), convection-diffusion (CD) and convection-diffusion-reaction (CDR) equations. These equations show multiscale behavior in reaction or convection dominated situations. The idea is based on the approximation of the definite integral of the interpolation function within the element, instead of the function approximation. The numerical experiments are performed using the bilinear Lagrangian elements. To validate the approach, the numerical results obtained for a benchmark problem are compared with the analytical solution in a wide range of Peclet and Damkohler numbers. The results show that the developed method is capable of generating stable and accurate solutions.