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Finite element method, Boundary value problems, Least squares, Integral equations


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.


NOTICE: this is the author’s version of a work that was accepted for publication in Mathematics of Computation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Mathematics of Computation, Volume 86, Number 307, September 2017, Pages 2261–2284. Article is available online at:

At the time of writing the article Michael Karkulik was affiliated with the Pontifical Catholic University of Chile.



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