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Open Access research with a European policy impact...

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EPRC is a leading institute in Europe for comparative research on public policy, with a particular focus on regional development policies. Spanning 30 European countries, EPRC research programmes have a strong emphasis on applied research and knowledge exchange, including the provision of policy advice to EU institutions and national and sub-national government authorities throughout Europe.

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A Petrov-Galerkin enriched method: a mass conservative finite element method for the Darcy equation

Barrenechea, G.R. and Franca, L.P. and Valentin, F. (2007) A Petrov-Galerkin enriched method: a mass conservative finite element method for the Darcy equation. Journal of Sound and Vibration, 196 (21-24). pp. 2449-2464. ISSN 0022-460X

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Abstract

Starting from the non-stable p1/p0 discretization we build enhanced methods for the Darcy equation which are stable and locally mass-conservative. The methods are derived in a Petrov-Galerkin framework where both velocity and pressure trial spaces are enriched with multiscale functions. These functions solve local problems correcting the residuals of the strong equations in each element and interior edge, which leads to a velocity space enhanced with functions belonging to the lowest order Raviart-Thomas space. Several numerical tests validate the methods.