Additive schwarz methods for indefinite hypersingular integral equations in R³ - the p-version

References

• Ben Belgacem , F. 1993 . Discrétisations 3D non conformed par la méthode de décomposition de domaine dés éléments avec joints: . analyse mathematique et mist en oeuvre pour le probleme de Poisson, PhD thesis . May 1993 , Paris VI, GA. Université Pierre et Marie Curie .
   Google Scholar
• Ben Belgacem , F. 1994 . Polynomial extensions of compatible polynomial traces in three dimensions . Methods Appl. Mech. Engrg , 116 : 235 – 241 . Proceedings of the International Conference On Spectral and High Order Methods 1992 (C. Bernardi and Y. Maday, eds.)
   Web of Science ®Google Scholar
• Bergh , J. and Löfström , J. 1976 . “ Interpolation Spaces ” . In No. 223 in Grundlehren der mathematischen Wissenschaften , Berlin : Springer-Verlag .
   Google Scholar
• Bramble , J. H. and Xu , J. 1991 . Some estimates for a weighted L2 projection . Math. Comp , 56 : 463 – 476 .
   Web of Science ®Google Scholar
• Cai , X.-C. and Wldlund , O. B. 1992 . Domain decomposition algorithms for indefinite elliptic problems . Siam J. Sci. Stat. Comput , 13 : 243 – 258 .
   Web of Science ®Google Scholar
• Canuto , C. and Funaro , D. 1988 . The Schwarz algorithm for spectral methods . SIAM J. Numer. Anal , 25 : 24 – 40 .
   Web of Science ®Google Scholar
• Chan , T. F. and Mathew , T. P. 1994 . Domain decomposition algorithms . Acta Numerica , 25 : 61 – 143 .
   Google Scholar
• Costabel , M. 1988 . Boundary integral operators on Lipschitz domains: Elementary results . SIAM J. Math. Anal , 19 : 613 – 626 .
   Web of Science ®Google Scholar
• Costabel , M. and Stephan , E. P. 1998 . Duality estimates for the numerical approximation of boundary integral equations . Numer. Math , 54 : 339 – 353 .
   Google Scholar
• Eisenstat , S. C. , Elman , H. C. and Schultz , M. H. 1983 . Variational iterative methods for non-symmetric systems of linear equations . SIAM J. Numer. Anal , 20 : 345 – 357 .
   Web of Science ®Google Scholar
• Grisvard , P. 1985 . Elliptic Problems in nonsmooth domains , Boston : Pitman Publishing Inc .
   Google Scholar
• Heuer , N. 1998 . An iterative sub structuring method for the p-version of the boundary element method for hypersingular integral equations in three dimensions . Numer. Math , 79 : 371 – 396 .
   Web of Science ®Google Scholar
• Hsiao , G. C. , Khoromskij , B. N. and Wendland , W. L. 1994 . “ Boundary integral operators and domain decomposition ” . In DFG Priority Research Boundary Element Methods , 94 – 11 . Germany : Universitat Stuttgart . Preprint
   Google Scholar
• Hsiao , G. C. and Wendland , W. L. 1977 . A finite element method for some integral equations of the first kind . J. Math. Anal , 58 : 449 – 481 .
   Web of Science ®Google Scholar
• Hsiao , G. C. and Wendland , W. L. 1991 . “ Domain decomposition in boundary element methods ” . In Domain Decomposition Methods for Partial Differential Equations , Edited by: Glowinski , R. , Kuznetsov , Y. A. , Meurant , G. A. , Périaux , J. and Widlund , O. B. 41 – 49 . Philadelphia : SIAM .
   Google Scholar
• Maday , Y. 1989 . Relevements de traces polynomials et interpolations Hilberiiennes entre espaces de polynomes . C. R. Acad. Sci. Paris Sér, I. Math , 309 : 463 – 468 .
   Google Scholar
• Maischak , M. 1995 . The analytical computation of the Galerkin elements for the Laplacé, Lame and Helmholtz equation in 3D-BEM, , 95 – 16 . DFG-Schwerpunkt Randelementmethoden .
   Google Scholar
• Pavarino , L. F. 1994 . Additive Schwarz methods for the pmdash;version finite element method . Numer. Math , 66 : 493 – 515 .
   Web of Science ®Google Scholar
• Pavarino , L. F. 1994 . Schwarz methods with local refinement for the p-version finite element method . Numer. Math , 69 : 185 – 211 .
   Web of Science ®Google Scholar
• Pavarino , L. F. and Widlund , O. B. 1996 . A polylogarithmic bound for an iterative substructuring method for spectral elements in three dimensions . SIAM J. Numer. Anal , 33 : 1303 – 1335 .
   Web of Science ®Google Scholar
• Saad , Y. and Schultz , M. H. 1986 . GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems . SIAM J. Sci. Stat. Comput , 7 : 856 – 869 .
   Web of Science ®Google Scholar
• Stephan , E. P. 1987 . Boundary integral equations for screen problems in R3 . Integral Equations Operator Theory , 10 : 257 – 263 .
   Web of Science ®Google Scholar
• Stephan , E. P. and Suri , M. 1991 . The h-p version of the boundary element method on polygonal domains with quasiuniform meshes . RAIRO Modél. Math. Anal. Numér , 25 : 783 – 807 .
   Web of Science ®Google Scholar
• Stephan , E. P. and Tran , T. 1998 . Domain decomposition algorithms for indefinite hypersingular integral equations-the h-and p-versions . SIAM J. Sci. Comput , 19 : 1139 – 1153 .
   Web of Science ®Google Scholar
• Stephan , E. P. and Wendland , W. L. 1976 . Remarks to Galerkin and least squares methods with finite elements for general elliptic problems . Manuscripta Geodaetica , 1 : 93 – 123 .
   Google Scholar
• Von Petersdorff , T. 1989 . Randwertprobleme der Elastizitätstheorie fur Polyeder-Singularitäten und Approximation mit Randelementmethoden . PhD thesis . 1989 , Germany. Technische Hochschule Darmstadt .
   Google Scholar
• Von Petersdorff , T. and Stephan , E. P. 1990 . Regularity of mixed boundary value problems in R3 and boundary element methods on graded meshes . Math. Methods Appl. Sci , 12 : 229 – 249 .
   Web of Science ®Google Scholar
• Wendland , W. L. 1990 . “ Boundary element methods for elliptic problems ” . In Mathematical Theory of Finite and Boundary Element Methods , Edited by: Schatz , A. H. , Thomée , V. and Wendland , W. L. Vol. 150 , 219 – 276 . Basel : Birkhäuser . DMV Seminar
   Google Scholar