Coupling of Nonconforming Finite Elements and Boundary Elements I: A Priori Estimates

Carstensen, Carsten; Funken, Stefan A.

doi:10.1007/s607-1999-8334-7

Cited by 14 publications

(40 citation statements)

References 16 publications

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“…This coupling procedure yields a symmetric operator system (change the sign of the second row to obtain symmetry and recall (4)). It is a variant of the symmetric coupling of [8,19] that can be found in [6] in the context of coupling non-conforming FEM and BEM.…”

Section: Non-homogeneous Penetrable Obstacles (1)mentioning

confidence: 99%

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Theoretical aspects of the application of convolution quadrature to scattering of acoustic waves

2009

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In this paper we address several theoretical questions related to the numerical approximation of the scattering of acoustic waves in two or three dimensions by penetrable non-homogeneous obstacles using convolution quadrature (CQ) techniques for the time variable and coupled boundary element method/finite element method for the space variable. The applicability of CQ to waves requires polynomial type bounds for operators related to the operator − s 2 in the right half complex plane. We propose a new systematic way of dealing with this problem, both at the continuous and semidiscrete-in-space cases. We apply the technique to three different situations: scattering by a group of sound-soft and -hard obstacles, by homogeneous and non-homogeneous obstacles.

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Section: Non-homogeneous Penetrable Obstacles (1)mentioning

confidence: 99%

“…The space discretization will be done by using an abstract Finite Element space for the interior variable and two Boundary Element spaces for unknowns on the interface. The coupling procedure will be the symmetric coupling with two equations and three unknowns as in [6]. The symmetric coupling procedure of [8] or [19] is studied in Sect.…”

mentioning

confidence: 99%

Theoretical aspects of the application of convolution quadrature to scattering of acoustic waves

2009

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“…Collecting the equations for the interior (1) & (2) and the exterior (4) & (5) together for both conforming and non-conforming cases and, for the latter, identifying the linear conforming functionsû ∈ S 1/2 with the linear non-conforming Crouzeix-Raviart functions u ∈ V NC h on the boundary B and introducing an extra pair of scalars to control constants appearing in the traction in a similar fashion to that used in [14], the full interior-exterior problem may be expressed as…”

Section: Coupled Interior-exteriormentioning

confidence: 99%

“…As can be seen from the results in Figure 3, at least a linear order of convergence, O(h), is achieved for both the velocity and pressure in the L 2 norm and for the velocity in the energy norm, with the discontinuous finite element-boundary element coupling scheme. Given its origins as essentially the extension, from a scalar to a vector-based non-conforming FEM-BEM coupling, of the method for a linear governing system of equations described in [14], this is in line with the theoretically expected rates for the original scheme [14]. Furthermore, an approximately quadratic, O(h 2 ), behaviour of the velocity in the L 2 norm, as seen and expected in the equivalent coupled formulations for the conforming case [20], may also be noted.…”

Section: Numerical Experimentsmentioning

confidence: 99%

FEM‐BEM coupling for the exterior Stokes problem with non‐conforming finite elements and an application to small droplet deformation dynamics

Radcliffe

2011

Numerical Methods in Fluids

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SUMMARYA non-conforming, discontinuous Galerkin finite element-boundary element coupling procedure is presented for the exterior planar Stokes problem. The novel coupled formulation is developed using that for the conforming case as a guide to the introduction of extra mortar variables used to couple a discontinuous interior finite element solution with a continuous exterior boundary element solution. Convergence results for the new scheme are presented, for a range of different interior penalties, on computational domains discretized with regular structured meshes.To illustrate an application, the excitations required to model two-phase droplet deformations in an extensional flow, under simple surface tension, with the new scheme are also presented. For a selection of different drop viscocities and exterior flows, with and without a rotational component, the progression to a steady-state deformation of initially undeformed circular drops is calculated and the results compared with those from both a conforming FEM-BEM equivalent scheme and from a small perturbation analysis where available.

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“…If the right-hand side is the same as (7), we obtain one of the solutions of (7). The solution of (1) can be recovered by:…”

Section: 3mentioning

confidence: 99%

Nonsymmetric coupling of BEM and mixed FEM on polyhedral interfaces

2010

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Abstract. In this paper we propose and analyze some new methods for coupling mixed finite element and boundary element methods for the model problem of the Laplace equation in free space or in the exterior of a bounded domain. As opposed to the existing methods, which use the complete matrix of operators of the Calderón projector to obtain a symmetric coupled system, we propose methods with only one integral equation. The system can be considered as a further generalization of the Johnson-Nédélec coupling of BEM-FEM to the case of mixed formulations in the bounded domain. Using some recent analytical tools we are able to prove stability and convergence of Galerkin methods with very general conditions on the discrete spaces and no restriction relating the finite and boundary element spaces. This can be done for general Lipschitz interfaces and in particular, the coupling boundary can be taken to be a Lipschitz polyhedron. Both the indirect and the direct approaches for the boundary integral formulation are explored.

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Coupling of Nonconforming Finite Elements and Boundary Elements I: A Priori Estimates

Cited by 14 publications

References 16 publications

Theoretical aspects of the application of convolution quadrature to scattering of acoustic waves

Theoretical aspects of the application of convolution quadrature to scattering of acoustic waves

FEM‐BEM coupling for the exterior Stokes problem with non‐conforming finite elements and an application to small droplet deformation dynamics

Nonsymmetric coupling of BEM and mixed FEM on polyhedral interfaces

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