Relationship between multiscale enrichment and stabilized finite element methods for the generalized Stokes problem

Barrenechea, Gabriel and Valentin, Frédéric (2005) Relationship between multiscale enrichment and stabilized finite element methods for the generalized Stokes problem. Comptes Rendus Mathematique, 341 (10). pp. 635-640. (https://doi.org/10.1016/j.crma.2005.09.038)

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Abstract

We derive a new stabilized finite element method for the generalized Stokes problem starting from the non-stable continuous finite element space enriched with multiscale functions. The stabilization parameter is related with the enrichment functions which are analytically computed from a boundary value problem at the element level leading to a method which is free of constants. Optimal error estimates are obtained in natural norms and numerical tests validate the method

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