Abstract
In this paper, an iterative substructuring method with Lagrange multipliers is proposed for discrete problems arising from approximation of elliptic problem in two dimensions on non-matching meshes. The problem is formulated using a mortar technique. The algorithm belongs to the family of dual-primal FETI (Finite Element Tearing and Interconnecting) methods which has been analyzed recently for discretization on matching meshes. In this method the unknowns at the vertices of substructures are eliminated together with those of the interior nodal points of these substructures. It is proved that the preconditioner proposed is almost optimal; it is also well suited for parallel computations.
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References
Ben Belgacem, F. (1999) The mortar finite element method with Lagrange multipliers. Numer. Math. 84, 173–197
Bernardi, C, Maday, Y., Patera, A. T. (1989) A new nonconforming approach to domain decomposition. The mortar element method. College de Prance Seminar, H. Brezis and J. L. Lions, eds., Pitman.
Farhat, C, Lesoinne, M., Pierson, K. (2000) A scalable dual - primal domain decomposition. Numer. Lin. Alg. App. Vol. 7(7–8), 687–714
Klawonn, A., Widlund, O. (2001) FETI and Neumann - Neumann iterative sub-structuring methods: Connections and new results. Comm. Pure. Appl. Math. 54, 57–90
Klawonn, A., Widlund, O., Dryja, M. (2001) Dual-primal FETI methods for three-dimensional elliptic problems with heterogeneous coefficients. Technical report 2001-815, Computer Science Department, Courant Institute of Mathematical Sciences
Mandel, J., Tezaur, R. (2001) On the convergence of a dual-primal substructuring method. Numer. Math. 88:3, 543–558
Peisker, P. (1988) On the numerical solution of the first biharmönic equation. MAN Mathematical Modelling and Numerical Analysis, 22, #4, 655–676
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© 2002 Springer-Verlag Berlin Heidelberg
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Dryja, M., Widlund, O.B. (2002). A FETI - DP Method for a Mortar Discretization of Elliptic Problems. In: Pavarino, L.F., Toselli, A. (eds) Recent Developments in Domain Decomposition Methods. Lecture Notes in Computational Science and Engineering, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56118-4_3
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DOI: https://doi.org/10.1007/978-3-642-56118-4_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43413-9
Online ISBN: 978-3-642-56118-4
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