A note on the polynomial approximation of vertex singularities in the boundary element method in three dimensions

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A note on the polynomial approximation of vertex singularities in the boundary element method in three dimensions

A. Bespalov

Source: J. Integral Equations Appl. Volume 21, Number 3 (2009), 359-380.

First Page: Show

Primary Subjects: 41A10, 65N15, 65N38

Keywords: $p$-approximation; $hp$-approximation on quasi-uniform meshes; boundary element method; singularities

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.jiea/1248269701
Digital Object Identifier: doi:10.1216/JIE-2009-21-3-359
Zentralblatt MATH identifier: 05612799
Mathematical Reviews number (MathSciNet): MR2529614

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References

M. Ainsworth, W. McLean, and T. Tran, The conditioning of boundary element equations on locally refined meshes and preconditioning by diagonal scaling, SIAM J. Numer. Anal., 36 (1999), 1901-1932.

Mathematical Reviews (MathSciNet): MR1712149

Zentralblatt MATH: 0947.65125

Digital Object Identifier: doi:10.1137/S0036142997330809

JSTOR: links.jstor.org

I. Babuška and M. Suri, The optimal convergence rate of the p-version of the finite element method, SIAM J. Numer. Anal., 24 (1987), 750-776.

Mathematical Reviews (MathSciNet): MR899702

Zentralblatt MATH: 0637.65103

Digital Object Identifier: doi:10.1137/0724049

JSTOR: links.jstor.org

J. Bergh and J. Löfström, Interpolation Spaces, no. 223 in Grundlehren der mathematischen Wissenschaften, Springer-Verlag, Berlin, (1976).

Mathematical Reviews (MathSciNet): MR482275

Zentralblatt MATH: 0344.46071

A. Bespalov and N. Heuer, The $p$-version of the boundary element method for hypersingular operators on piecewise plane open surfaces, Numer. Math., 100 (2005), 185-209.

Mathematical Reviews (MathSciNet): MR2135781

Zentralblatt MATH: 1082.65129

Digital Object Identifier: doi:10.1007/s00211-005-0590-9

--------, The $p$-version of the boundary element method for weakly singular operators on piecewise plane open surfaces, Numer. Math., 106 (2007), 69-97.

Mathematical Reviews (MathSciNet): MR2286007

Zentralblatt MATH: 1117.65160

Digital Object Identifier: doi:10.1007/s00211-006-0058-6

--------, The $hp$-version of the boundary element method with quasi-uniform meshes in three dimensions, ESAIM: Mathematical Modelling and Numerical Analysis, 42 (2008), 821--849.

Mathematical Reviews (MathSciNet): MR2454624

Digital Object Identifier: doi:10.1051/m2an:2008025

Zentralblatt MATH: 1154.41300

--------, The $hp$-version of the boundary element method with quasi-uniform meshes for weakly singular operators on surfaces, IMA J. Numer. Anal. (to appear).

--------, Natural $p$-BEM for the electric field integral equation on screens, IMA J. Numer. Analysis (to appear).

P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, (1978).

Mathematical Reviews (MathSciNet): MR520174

M. Costabel and M. Dauge, Singularities of electromagnetic fields in polyhedral domains, Arch. Rational Mech. Anal., 151 (2000), 221-276.

Mathematical Reviews (MathSciNet): MR1753704

Zentralblatt MATH: 0968.35113

Digital Object Identifier: doi:10.1007/s002050050197

M. Costabel and E. P. Stephan, A direct boundary integral equation method for transmission problems, J. Math. Anal. Appl., 106 (1985), 367-413.

Mathematical Reviews (MathSciNet): MR782799

Zentralblatt MATH: 0597.35021

Digital Object Identifier: doi:10.1016/0022-247X(85)90118-0

I. M. Gel'fand and G. E. Shilov, Generalized functions. Vol. I: Properties and operations, Academic Press, New York, (1964).

Mathematical Reviews (MathSciNet): MR166596

P. Grisvard, Elliptic Problems in Nonsmooth Domains, Pitman Publishing Inc., Boston, (1985).

Mathematical Reviews (MathSciNet): MR775683

Zentralblatt MATH: 0695.35060

W. McLean, Strongly Elliptic Systems and Boundary Integral Equations, Cambridge University Press, (2000).

Mathematical Reviews (MathSciNet): MR1742312

Zentralblatt MATH: 0948.35001

C. Schwab and M. Suri, The optimal p-version approximation of singularities on polyhedra in the boundary element method, SIAM J. Numer. Anal., 33 (1996), 729-759.

Mathematical Reviews (MathSciNet): MR1388496

Zentralblatt MATH: 0854.65108

Digital Object Identifier: doi:10.1137/0733037

JSTOR: links.jstor.org

E. Stephan, Solution procedures for interface problems in acoustics and electromagnetics, in Theoretical acoustics and numerical techniques, vol. 277 of CISM Courses and Lectures, Springer, Vienna, (1983), 291-348.

Mathematical Reviews (MathSciNet): MR762832

Zentralblatt MATH: 0578.76078

T. von Petersdorff and E. P. Stephan, Decompositions in edge and corner singularities for the solution of the Dirichlet problem of the Laplacian in a polyhedron, Math. Nachr., 149 (1990), 71-104.

Mathematical Reviews (MathSciNet): MR1124795

--------, Regularity of mixed boundary value problems in $\R^3$ and boundary element methods on graded meshes, Math. Methods Appl. Sci., 12 (1990), 229-249.

Mathematical Reviews (MathSciNet): MR1043756

Zentralblatt MATH: 0722.35017

Digital Object Identifier: doi:10.1002/mma.1670120306

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