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Published in:
2013 | OriginalPaper | Chapter
Coupling Hdiv an H1 Finite Element Approximations for a Poisson Problem
Authors : D. de Siqueira, P. R. B. Devloo, S. M. Gomes
Published in: Numerical Mathematics and Advanced Applications 2011
Publisher: Springer Berlin Heidelberg
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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.