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Mathematics of Computation

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On the coupling of DPG and BEM


Authors: Thomas Führer, Norbert Heuer and Michael Karkulik
Journal: Math. Comp.
MSC (2010): Primary 65N30, 35J20, 65N38
DOI: https://doi.org/10.1090/mcom/3170
Published electronically: December 21, 2016
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Abstract: We develop and analyze strategies to couple the discontinuous Petrov-Galerkin method with optimal test functions to (i) least-squares boundary elements and (ii) various variants of standard Galerkin boundary elements. An essential feature of our method is that, despite the use of boundary integral equations, optimal test functions have to be computed only locally. We apply our findings to a standard transmission problem in full space and present numerical experiments to validate our theory.


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Additional Information

Thomas Führer
Affiliation: Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Santiago, Chile
Email: tofuhrer@mat.uc.cl

Norbert Heuer
Affiliation: Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Santiago, Chile
Email: nheuer@mat.uc.cl

Michael Karkulik
Affiliation: Department of Mathematics and Statistics, Portland State University, Portland, Oregon 97207-0751
Address at time of publication: Departamento de Matemática, Universidad Técnica Federico Santa María, Avenida España 1680, Valparaíso, Chile
Email: michael.karkulik@usm.cl

DOI: https://doi.org/10.1090/mcom/3170
Keywords: Transmission problem, DPG method with optimal test functions, boundary elements, least-squares method, coupling, ultra-weak formulation, Calder\'on projector
Received by editor(s): August 3, 2015
Received by editor(s) in revised form: August 4, 2015, and March 18, 2016
Published electronically: December 21, 2016
Additional Notes: The authors were supported by CONICYT through FONDECYT projects 1150056, 3140614, 3150012, and Anillo ACT1118 (ANANUM), and by NSF under grant DMS-1318916
Article copyright: © Copyright 2016 American Mathematical Society