Coupling Hdiv an H1 Finite Element Approximations for a Poisson Problem

D. de Siqueira (), P. R. B. Devloo () and S. M. Gomes ()
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D. de Siqueira: IMECC-Unicamp
P. R. B. Devloo: FEC-Unicamp
S. M. Gomes: IMECC-Unicamp

A chapter in Numerical Mathematics and Advanced Applications 2011, 2013, pp 411-417 from Springer

Abstract: Abstract The purpose of the paper is to approximate an elliptic problem coupling two different formulations. The domain is split into two non-overlapping sub-domains. On the first one, the problem is approximated using classical Galerkin method where the primal solution p is searched in H 1 approximation spaces. On the other one, the mixed formulation is applied, which is based on Hdiv and L 2 approximation spaces for the dual ∇ p and primal p solutions, respectively. On the interface, the continuity of p and ∇ p is imposed strongly, using transmission conditions. The resulting coupled formulation is a saddle point problem, which is solved for high order hierarchical approximation spaces. Numerical simulations for a test problem show consistent rates of convergence when compared with the corresponding classical and mixed formulations in the whole domain.

Keywords: Poisson Problem; Approximation Space; Mixed Formulation; Classical Galerkin Formulation; Saddle Point Problem (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-33134-3_44

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DOI: 10.1007/978-3-642-33134-3_44

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