An a priori error analysis for the coupling of local discontinuous Galerkin and boundary element methods

Authors:
Gabriel N. Gatica and Francisco-Javier Sayas

Journal:
Math. Comp. **75** (2006), 1675-1696

MSC (2000):
Primary 65N30, 65N38, 65N12, 65N15

DOI:
https://doi.org/10.1090/S0025-5718-06-01864-3

Published electronically:
July 3, 2006

MathSciNet review:
2240630

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Abstract: In this paper we analyze the coupling of local discontinuous Galerkin (LDG) and boundary element methods as applied to linear exterior boundary value problems in the plane. As a model problem we consider a Poisson equation in an annular polygonal domain coupled with a Laplace equation in the surrounding unbounded exterior region. The technique resembles the usual coupling of finite elements and boundary elements, but the corresponding analysis becomes quite different. In particular, in order to deal with the weak continuity of the traces at the interface boundary, we need to define a mortar-type auxiliary unknown representing an interior approximation of the normal derivative. We prove the stability of the resulting discrete scheme with respect to a mesh-dependent norm and derive a Strang-type estimate for the associated error. Finally, we apply local and global approximation properties of the subspaces involved to obtain the a priori error estimate in the energy norm.

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Additional Information

**Gabriel N. Gatica**

Affiliation:
Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile

Email:
ggatica@ing-mat.udec.cl

**Francisco-Javier Sayas**

Affiliation:
Departamento de Matemática Aplicada, Universidad de Zaragoza, Centro Politécnico Superior, María de Luna, 3 - 50018 Zaragoza, Spain

Email:
jsayas@unizar.es

DOI:
https://doi.org/10.1090/S0025-5718-06-01864-3

Keywords:
Boundary elements,
local discontinuous Galerkin,
coupling,
error estimates

Received by editor(s):
January 3, 2005

Received by editor(s) in revised form:
August 31, 2005

Published electronically:
July 3, 2006

Additional Notes:
This research was partially supported by CONICYT-Chile through the FONDAP Program in Applied Mathematics, by the Dirección de Investigación of the Universidad de Concepción through the Advanced Research Groups Program, by Spanish FEDER/MCYT Project MTM2004-019051, and by a grant of Programa Europa XXI (Gobierno Aragón + CAI)

Article copyright:
© Copyright 2006
American Mathematical Society