Stable Boundary Element Approximations of Steklov-Poincaré Operators

Mathematical Aspects of Boundary Element Methods

Volumn , Issue , 2024, Pages 296-305

  Steinbach, O ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

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EID: 85201878448     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1201/9780429332449-25     Document Type: Chapter

References (12)

1. V. I. Agoshkov: Poincaré–Steklov’s operators and domain decomposition methods in finite dimensional spaces. In: First International Symposium on Domain Decomposition Methods for Partial Differential Equations (R. Glowinski et. al. eds.), SIAM, Philadelphia, 73-112, 1988.
2. M. Costabel: Boundary integral operators on Lipschitz domains: Elementary results. SIAM J. Numer. Anal. 19 (1988) 613-626.
3. M. Costabel, E. P. Stephan: Boundary integral equations for mixed boundary value problems in polygonal domains and Galerkin approximation. Banach Centre Publications, Warsaw, 15 (1985) 175-251.
4. G. C. Hsiao, E. Schnack, W. L. Wendland: Hybrid coupled finite–boundary element methods for elliptic systems of second order. Preprint 98/13, SFB 404, Universität Stuttgart, 1998.
5. G. C. Hsiao, E. P. Stephan, W. L. Wendland: On the integral equation method for the plane mixed boundary value problem of the Laplacian. Math. Meth. Appl. Sci. 1 (1979) 265–321.
6. A. Quarteroni, A. Valli: Numerical Approximation of Partial Differential Equations. Springer, Berlin, 1994.
7. G. Schmidt: Boundary element discretization of Poincaré–Steklov operators. Numer. Math. 69 (1994) 83-101.
8. O. Steinbach: A note on initial higher order convergence results for boundary element methods with approximated boundary conditions. Submitted, 1996.
9. O. Steinbach: On a hybrid boundary element method. Numer. Math., accepted, 1998.
10. O. Steinbach: Mixed approximations for boundary elements. Submitted, 1999.
11. O. Steinbach, W. L. Wendland: Domain Decomposition and Boundary Elements. In: Proceedings of NMA98, Sofia, 1998.
12. W. L. Wendland: On asymptotic error estimates for combined BEM and FEM. In: Finite Element and Boundary Element Techniques from Mathematical and Engineering Point of View (E. Stein, W. L. Wendland eds.), Springer, Berlin, 273-333, 1988.