A Note on the Stable One-Equation Coupling of Finite and Boundary Elements | Zendy

Olaf Steinbach | Zendy

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A Note on the Stable One-Equation Coupling of Finite and Boundary Elements

Author(s) -

Olaf Steinbach

Publication year - 2011

Publication title -

siam journal on numerical analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.78

H-Index - 134

eISSN - 1095-7170

pISSN - 0036-1429

DOI - 10.1137/090762701

Subject(s) - mathematics , lipschitz continuity , finite element method , boundary (topology) , discretization , mathematical analysis , galerkin method , bilinear interpolation , stability (learning theory) , mathematical proof , coupling (piping) , integral equation , geometry , mechanical engineering , physics , machine learning , computer science , engineering , thermodynamics , statistics

In a recent paper [SIAM J. Numer. Anal., 47 (2009), pp. 3451-3463] Sayas proved the stability of the Johnson-Nédélec coupling of finite and boundary element methods on polygonal interfaces when the direct boundary integral equation with single and double layer integral operators is used only. In this note we present two alternative proofs of this result for general Lipschitz interfaces. In particular, we prove an ellipticity estimate of the coupled bilinear form. Hence, we can use standard arguments to derive stability and error estimates for the Galerkin discretization for all pairs of finite and boundary element trial spaces.

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