Coupling of Raviart-Thomas and hybridizable discontinuous Galerkin methods with BEM

Bernardo Cockburn; Johnny Guzman; Francisco Javier Sayas

doi:10.1137/100818339

Coupling of Raviart-Thomas and hybridizable discontinuous Galerkin methods with BEM

Bernardo Cockburn, Johnny Guzman, Francisco Javier Sayas

School of Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

We present new a priori error analyses of the coupling of the Raviart-Thomas (RT) method and BEM as well as of the coupling of the hybridizable discontinuous Galerkin (HDG) method with BEM. The novel features of the analysis of the RT-BEM coupling are the superconvergence estimates for the scalar approximation of the interior problem and new bounds in weak and strong norms for the boundary variables. The analysis of the HDG-BEM coupling is the first analysis of this coupling and shows that the coupling provides approximations with the same convergence properties as those of the RT-BEM coupling.

Original language	English (US)
Pages (from-to)	2778-2801
Number of pages	24
Journal	SIAM Journal on Numerical Analysis
Volume	50
Issue number	5
DOIs	https://doi.org/10.1137/100818339
State	Published - 2012

Keywords

Boundary element methods
Coupling
Discontinuous Galerkin methods
Mixed finite element

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10.1137/100818339

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title = "Coupling of Raviart-Thomas and hybridizable discontinuous Galerkin methods with BEM",

abstract = "We present new a priori error analyses of the coupling of the Raviart-Thomas (RT) method and BEM as well as of the coupling of the hybridizable discontinuous Galerkin (HDG) method with BEM. The novel features of the analysis of the RT-BEM coupling are the superconvergence estimates for the scalar approximation of the interior problem and new bounds in weak and strong norms for the boundary variables. The analysis of the HDG-BEM coupling is the first analysis of this coupling and shows that the coupling provides approximations with the same convergence properties as those of the RT-BEM coupling.",

keywords = "Boundary element methods, Coupling, Discontinuous Galerkin methods, Mixed finite element",

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T1 - Coupling of Raviart-Thomas and hybridizable discontinuous Galerkin methods with BEM

AU - Cockburn, Bernardo

AU - Guzman, Johnny

AU - Sayas, Francisco Javier

PY - 2012

Y1 - 2012

N2 - We present new a priori error analyses of the coupling of the Raviart-Thomas (RT) method and BEM as well as of the coupling of the hybridizable discontinuous Galerkin (HDG) method with BEM. The novel features of the analysis of the RT-BEM coupling are the superconvergence estimates for the scalar approximation of the interior problem and new bounds in weak and strong norms for the boundary variables. The analysis of the HDG-BEM coupling is the first analysis of this coupling and shows that the coupling provides approximations with the same convergence properties as those of the RT-BEM coupling.

AB - We present new a priori error analyses of the coupling of the Raviart-Thomas (RT) method and BEM as well as of the coupling of the hybridizable discontinuous Galerkin (HDG) method with BEM. The novel features of the analysis of the RT-BEM coupling are the superconvergence estimates for the scalar approximation of the interior problem and new bounds in weak and strong norms for the boundary variables. The analysis of the HDG-BEM coupling is the first analysis of this coupling and shows that the coupling provides approximations with the same convergence properties as those of the RT-BEM coupling.

KW - Boundary element methods

KW - Coupling

KW - Discontinuous Galerkin methods

KW - Mixed finite element

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JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

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Coupling of Raviart-Thomas and hybridizable discontinuous Galerkin methods with BEM

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Keywords

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