Galerkin-Kollokation für eine verbesserte Randelement-Methode für ein ebenes gemischtes Randwertproblem

Lamp, U.; Schleicher, T.; Stephan, Ernst P.; Wendland, Wolfgang L.

doi:10.1007/bf02242273

Cited by 28 publications

(6 citation statements)

References 8 publications

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“…Nor can we do justice to the large body of recent work on (Cauchy) singular integral equations in the plane (see, for example, Prossdorf andSilbermann (1977, 1991), Prossdorf (1989)). Mixed boundary value problems will be ignored (see Wendland et al (1979), Lamp et al (1984), Stephan and Wendland (1985), McLean (1990)). And we will have nothing to say about another topic currently attracting considerable interest, namely nonlinear aspects of BIE (see Ruotsalainen and Wendland (1988), Ruotsalainen and Saranen (1989), Atkinson and Chandler (1990), Eggermont and Saranen (1990), Ruotsalainen (1992); and, in connection with coupling of BIEs and PDEs, Gatica and Hsiao (1989)).…”

Section: Introductionmentioning

confidence: 99%

Error analysis of boundary integral methods

Sloan¹

1992

Acta Numerica

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Many of the boundary value problems traditionally cast as partial differential equations can be reformulated as integral equations over the boundary. After an introduction to boundary integral equations, this review describes some of the methods which have been proposed for their approximate solution. It discusses, as simply as possible, some of the techniques used in their error analysis, and points to areas in which the theory is still unsatisfactory.

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Section: Introductionmentioning

confidence: 99%

Error analysis of boundary integral methods

Sloan¹

1992

Acta Numerica

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“…Some of the results, including orders of convergence, were displayed in [21] and for the case of the unit circle also in [16].…”

Section: : H-~ + ~(F) ~ H ~ +"(R)mentioning

confidence: 99%

Duality estimates for the numerical solution of integral equations

Costabel

Stephan

1989

Numer. Math.

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Summary.We formulate and prove Aubin-Nitsche-type duality estimates for the error of general projection methods. Examples of applications include collocation methods and augmented Galerkin methods for boundary integral equations on plane domains with corners and three-dimensional screen and crack problems. For some of these methods, we obtain higher order error estimates in negative norms in cases where previous formulations of the duality arguments were not applicable.

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“…where ξ = u 1 1 u2 , η = u 1 u 3 1 u4 , and (k nΦ )(ξ, η) :=k n (ξ, η − ξ)Φ(ξ, η) with χ(ξ) = χ (i) (ξ), χ(η) = χ (j) (η) (see (19), (20)). …”

Section: Theorem 4 Let π Hmentioning

confidence: 99%

Integration of singular Galerkin-type boundary element integrals for 3D elasticity problems

Andrä¹,

Schnack²

1997

Numerische Mathematik

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A Galerkin approximation of both strongly and hypersingular boundary integral equation (BIE) is considered for the solution of a mixed boundary value problem in 3D elasticity leading to a symmetric system of linear equations. The evaluation of Cauchy principal values (v. p.) and finite parts (p. f.) of double integrals is one of the most difficult parts within the implementation of such boundary element methods (BEMs). A new integration method, which is strictly derived for the cases of coincident elements as well as edge-adjacent and vertex-adjacent elements, leads to explicitly given regular integrand functions which can be integrated by the standard Gauss-Legendre and Gauss-Jacobi quadrature rules. Problems of a wide range of integral kernels on curved surfaces can be treated by this integration method. We give estimates of the quadrature errors of the singular four-dimensional integrals. Subject Classification (1991): 65N38,65D30,65R20,65N30 Mathematics

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Galerkin-Kollokation für eine verbesserte Randelement-Methode für ein ebenes gemischtes Randwertproblem

Cited by 28 publications

References 8 publications

Error analysis of boundary integral methods

Error analysis of boundary integral methods

Duality estimates for the numerical solution of integral equations

Integration of singular Galerkin-type boundary element integrals for 3D elasticity problems

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