Coupling Finite Elements and Auxiliary Sources
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2018-02
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Report
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Abstract
We consider second-order scalar elliptic boundary value problems on unbounded domains, which model, for instance, electrostatic fields. We propose a discretization that relies on a Trefftz approximation by multipole auxiliary sources in some parts of the domain and on standard mesh-based primal Lagrangian finite elements in other parts. Several approaches are developed and, based on variational saddle point theory, rigorously analyzed to couple both discretizations across the common interface: (1) least-squares-based coupling using techniques from PDE-constrained optimization; (2) coupling through Dirichlet-to-Neumann operators; and (3) three-field variational formulation in the spirit of mortar finite element methods. We compare these approaches in a series of numerical experiments.
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published
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2018-04
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Seminar for Applied Mathematics, ETH Zurich
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Subject
Finite element method; Multiple Multipole Program; Method of auxiliary sources; Trefftz method; Computational electromagentics
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03632 - Hiptmair, Ralf / Hiptmair, Ralf