Journal ArticleDOI
Is the one-equation coupling of finite and boundary element methods always stable?
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In this paper, a sufficient and necessary condition to ensure the ellipticity of the bilinear form of a second order uniform elliptic partial differential equation in the case of general Lipschitz interfaces is presented.Abstract:
In this paper we present a sufficient and necessary condition to ensure the ellipticity of the bilinear form which is related to the one-equation coupling of finite and boundary element methods to solve a scalar free space transmission problem for a second order uniform elliptic partial differential equation in the case of general Lipschitz interfaces. This condition relates the minimal eigenvalue of the coefficient matrix in the bounded interior domain to the contraction constant of the shifted double layer integral operator which reflects the shape of the interface. This paper extends and improves earlier results [12] on sufficient conditions, but now includes also necessary conditions. Numerical examples confirm the theoretical results on the sharpeness of the presented estimates.read more
Citations
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Journal ArticleDOI
Convergence of adaptive 3D BEM for weakly singular integral equations based on isotropic mesh-refinement
Michael Karkulik,Dirk Praetorius +1 more
TL;DR: It is proved that the usual adaptive mesh‐refining algorithm drives the corresponding error estimator to zero, and the sequence of discrete solutions thus tends to the exact solution within the energy norm.
Journal ArticleDOI
On Existence analysis of steady flows of generalized Newtonian fluids with concentration dependent power-law index
TL;DR: In this paper, the existence of a weak solution for certain class of models by using a generalization of the monotone operator theory was proved for generalized Sobolev spaces with variable exponent.
Journal ArticleDOI
Optimal preconditioning for the symmetric and nonsymmetric coupling of adaptive finite elements and boundary elements
TL;DR: A multilevel diagonal additive Schwarz preconditioner for the adaptive coupling of FEM and BEM for a linear 2D Laplace transmission problem is analyzed and it is rigorously proved that the condition number of the preconditionsed system stays uniformly bounded.
Journal ArticleDOI
On the ellipticity of coupled finite element and one-equation boundary element methods for boundary value problems
TL;DR: This paper extends some recent results on the stability of the Johnson–Nédelec coupling of finite and boundary element methods in the case of boundary value problems and several techniques for the stabilization of the coupled formulations are analysed.
Journal ArticleDOI
Convergence of adaptive BEM and adaptive FEM-BEM coupling for estimators without h-weighting factor
TL;DR: It is proved that in either case the usual adaptive algorithm drives the associated error estimator to zero, which is not even globally equivalent to weighted-residual error estimators for which recently convergence with quasi-optimal algebraic rates has been derived.
References
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Journal ArticleDOI
On the coupling of boundary integral and finite element methods
Claes Johnson,J.-Claude Nédélec +1 more
TL;DR: In this article, the error estimates for a procedure obtained by combining the boundary integral method and the usual finite element method are shown. But they are only for a special case of the problem described in this paper.
Journal ArticleDOI
A finite element method for some integral equations of the first kind
TL;DR: In this paper, a finite element approximation for a class of singular integral equations of the first kind was discussed. But the convergence rate of the Galerkin method with finite elements as trial functions is not known.
Book
Numerical Approximation Methods for Elliptic Boundary Value Problems. Finite and Boundary Elements
TL;DR: In this article, the authors present a method for solving boundary value problems using boundary integral operators and domain decomposition methods, as well as approximate methods and iterative solution methods, and fast boundary element methods.
Book ChapterDOI
Symmetric Methods for the Coupling of Finite Elements and Boundary Elements (Invited contribution)
TL;DR: In many applications, boundary element methods can only be used in combination with finite elements which cover that part of the domain where inhomogeneities or nonlinearities are located.