2012
DOI: 10.1137/100818339
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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 provide… Show more

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Cited by 13 publications
(11 citation statements)
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“…During his Zaragoza period, Javier had been interested in the coupling of LDG and BE methods [2,45,46]. During his Minneapolis period, he continued to develop this interest in three papers published in 2012, namely, on the coupling of the RT or HDG with BE methods [23], on general symmetric couplings of DG and BE methods [29], and on coupling at a distance HDG and BE methods [31]. During his Delaware period, he worked on nonsymmetric couplings of HDG and BE methods in the 2017 paper [44].…”
Section: Coupling Hdg and Boundary Element Methodsmentioning
confidence: 99%
“…During his Zaragoza period, Javier had been interested in the coupling of LDG and BE methods [2,45,46]. During his Minneapolis period, he continued to develop this interest in three papers published in 2012, namely, on the coupling of the RT or HDG with BE methods [23], on general symmetric couplings of DG and BE methods [29], and on coupling at a distance HDG and BE methods [31]. During his Delaware period, he worked on nonsymmetric couplings of HDG and BE methods in the 2017 paper [44].…”
Section: Coupling Hdg and Boundary Element Methodsmentioning
confidence: 99%
“…The classical bending-dominated problem of Cook's membrane 78 is revisited to take into account two materials with different mechanical properties as proposed in. 77 The tapered plate Ω defined by the points (0, 0), (48,44), (48,60), (0, 44) is decomposed in two nonoverlapping subdomains such that Ω CG is the convex region identified by the points (12, 20.25), (36, 38.75), (36, 50.25), (12, 38.75) and Ω HDG =Ω \ Ω CG . The first three levels of mesh refinement are displayed in Figure 9, where the subdomain Ω CG is represented in red, Ω HDG in blue and the interface Γ I in black.…”
Section: Bimaterials Cook's Membrane Problemmentioning
confidence: 99%
“…HDG methods were proposed by Cockburn et al in [11] as an improvement of traditional discontinuous Galerkin (DG) methods and have many applications; see, e.g., [8,9,12,13,15,16,32]. HDG methods are based on mixed formulations and introduce a new variable to approximate the trace of the scalar variable along the element boundary.…”
Section: A Class Of Embedded Dg Formulationsmentioning
confidence: 99%