A direct coupling of local discontinuous Galerkin and boundary element methods

The coupling of local discontinuous Galerkin (LDG) and boundary element methods (BEM), which has been developed recently to solve linear and nonlinear exterior transmission problems, employs a mortar-type auxiliary unknown to deal with the weak continuity of the traces at the interface boundary. As a consequence, the main features of LDG and BEM are maintained and hence the coupled approach benefits from the advantages of both methods. In this paper we propose a direct procedure that, instead of a mortar variable, makes use of a finite element subspace whose functions are required to be continuous only on the coupling boundary. In this way, the normal derivative becomes the only boundary unknown, and hence the total number of unknown functions is reduced by two. We prove the stability of the new discrete scheme and derive an a priori error estimate in the energy norm. The analysis is also extended to the case of nonlinear problems. Key words: boundary elements, local discontinuous Gal...

• Type: Journal
• Year: 2010
• Where: MOC
• Authors: Gabriel N. Gatica, Norbert Heuer, Francisco-Javier Sayas
• Keywords: Boundary Element Methods, Boundary Elements, Local Discontinuous Galerkin, MOC 2010, Security Privacy