On a Full Discretization Scheme for a Hypersingular Boundary Integral Equation over Smooth Curves | Zendy

Ralf Kieser | Zendy; Bernd H. Kleemann | Zendy; Andreas Rathsfeld | Zendy

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On a Full Discretization Scheme for a Hypersingular Boundary Integral Equation over Smooth Curves

Author(s) -

Ralf Kieser,

Bernd H. Kleemann,

Andreas Rathsfeld

Publication year - 1992

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/598

Subject(s) - mathematics , sobolev space , mathematical analysis , discretization , quadrature (astronomy) , integral equation , nyström method , galerkin method , boundary (topology) , gaussian quadrature , neumann boundary condition , domain (mathematical analysis) , nonlinear system , physics , electrical engineering , quantum mechanics , engineering

In this paper we consider a quadrature method for a hypersingular integral equation arising from a boundary integral formulation for the Neumann problem in a two-dimensional domain with smooth boundary. We prove that this method is equivalent to the trigonometric.Galerkin method. Consequently, we obtain stability and asymptotic error estimates in the scale of Sobolev spaces. Finally, we present some numerical tests.

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