Summary
We propose a new stabilized three-field formulation applied to the advection-diffusion equation. Using finite elements with SUPG stabilization in the interior of the subdomains our approach enables us to use almost arbitrary discrete function spaces. They need not to satisfy the inf-sup conditions of the standard three-field formulation. The scheme is stable and satisfies an optimal a priori estimate. Furthermore, we show how the scheme can be solved efficiently in parallel by an adapted Schur complement equation and an alternating Schwarz algorithm. Finally some numerical experiments confirm our theoretical results.
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Rapin, G., Lube, G. (2005). A Stabilized Three-Field Formulation and its Decoupling for Advection-Diffusion Problems. In: Barth, T.J., et al. Domain Decomposition Methods in Science and Engineering. Lecture Notes in Computational Science and Engineering, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26825-1_26
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DOI: https://doi.org/10.1007/3-540-26825-1_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22523-2
Online ISBN: 978-3-540-26825-3
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