On the coupling of boundary integral and finite element methods
Claes Johnson,J.-Claude Nédélec +1 more
TLDR
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.Abstract:
We prove some error estimates for a procedure obtained by combining the boundary integral method and the usual finite element method.read more
Citations
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Book
Finite Element Analysis of Acoustic Scattering
TL;DR: A cognitive journey towards the reliable simulation of scattering problems using finite element methods, with the pre-asymptotic analysis of Galerkin FEM for the Helmholtz equation with moderate and large wave number forming the core of this book, is described in this article.
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Non-reflecting boundary conditions
TL;DR: In this article, the use of nonreflecting boundary conditions in numerical solution of wave problems is reviewed, including local and non-local boundary conditions, as well as special procedures which involve artificial boundaries.
Journal ArticleDOI
A multiscale finite-element method
Ernst Rank,R. Krause +1 more
TL;DR: It is demonstrated how a block-iteration allows a simple and efficient implementation of the method and how finite element meshes can be constructed adaptively on the local and the global scales.
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A finite element method for large domains
Dan Givoli,Joseph B. Keller +1 more
TL;DR: In this article, a combined analytical and numerical method is devised to solve elliptic boundary value problems in large or infinite domains, where the domain is divided by an artificial boundary B into a small computational domain Ω and an infinite residual domain D in which the problem is solved analytically, and from the solution an exact nonlocal relation between the solution and its derivatives on B is deduced.
Book
Trefftz and Collocation Methods
TL;DR: In this article, the authors present a comprehensive review of boundary integral equation and boundary element methods and compare them with other kinds of boundary methods, including CTM, CM, and CTM coupling techniques.
References
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The Finite Element Method for Elliptic Problems
Philippe G. Ciarlet,J. T. Oden +1 more
TL;DR: The finite element method has been applied to a variety of nonlinear problems, e.g., Elliptic boundary value problems as discussed by the authors, plate problems, and second-order problems.
Journal ArticleDOI
The coupling of the finite element method and boundary solution procedures
TL;DR: The finite element method is now recognized as a general approximation process which is applicable to a variety of engineering problems and boundary solution procedures have been introduced as an independent alternative which at times is more economical and possesses certain merits as mentioned in this paper.
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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.