The h-p version of the boundary element method on polygonal domains with quasiuniform meshes
ESAIM: Modélisation mathématique et analyse numérique, Tome 25 (1991) no. 6, pp. 783-807. 
@article{M2AN_1991__25_6_783_0,
     author = {Stephan, E. P. and Suri, M.},
     title = {The $h-p$ version of the boundary element method on polygonal domains with
quasiuniform meshes},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {783--807},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {25},
     number = {6},
     year = {1991},
     mrnumber = {1135993},
     zbl = {0744.65073},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1991__25_6_783_0/}
}
TY  - JOUR
AU  - Stephan, E. P.
AU  - Suri, M.
TI  - The $h-p$ version of the boundary element method on polygonal domains with
quasiuniform meshes
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1991
SP  - 783
EP  - 807
VL  - 25
IS  - 6
PB  - AFCET - Gauthier-Villars
PP  - Paris
UR  - http://www.numdam.org/item/M2AN_1991__25_6_783_0/
LA  - en
ID  - M2AN_1991__25_6_783_0
ER  - 
%0 Journal Article
%A Stephan, E. P.
%A Suri, M.
%T The $h-p$ version of the boundary element method on polygonal domains with
quasiuniform meshes
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1991
%P 783-807
%V 25
%N 6
%I AFCET - Gauthier-Villars
%C Paris
%U http://www.numdam.org/item/M2AN_1991__25_6_783_0/
%G en
%F M2AN_1991__25_6_783_0
Stephan, E. P.; Suri, M. The $h-p$ version of the boundary element method on polygonal domains with
quasiuniform meshes. ESAIM: Modélisation mathématique et analyse numérique, Tome 25 (1991) no. 6, pp. 783-807. http://www.numdam.org/item/M2AN_1991__25_6_783_0/

[1] E. Alarcon, L. Abia, A. Reverter, On the possibility of adaptive boundary elements, in : Accuracy Estimates and Adaptive Refinements in Finite Element Computations (AFREC), Lisbon, 1984.

[2] E. Alarcon, A. Reverter, J. Molina, Hierarchical boundary elements. Comput. and Structures, 20 (1985) 151-156. | Zbl

[3] E. Alarcon, A. Reverter, p-adaptive boundary elements. Internat. J.Numer. Methods Engrg. 23 (1986) 801-829. | Zbl

[4] I. Babuška, M. Suri, The p and h-p versions of the finite element method, An Overview. Computer Methods in Applied Mechanics and Engineering 80 (1990) 5-26. | MR | Zbl

[5] I. Babuška, A. K. Aziz, Survey lectures on the mathematical foundations of the finite element method, in : The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (ed. by A. K. Aziz), Academic Press, New York (1972) 3-359. | MR | Zbl

[6] I. Babuška, M. Dorr, Error estimates for the combined h and p version of the finite element method. Numer. Math. 37 (1981) 257-277. | MR | Zbl

[7] I. Babuška, B. Guo, M. Suri, Implementation of non-homogeneous Dirichleboundary conditions in the p-version of the finite element method. Impact of Computing in Science and Engineering 1 (1989) 36-63. | Zbl

[8] I. Babuška, B. A. Szabo, I. N. Katz, The p-version of the finite element method. SIAM J. Numer. Anal. 18 (1981) 515-545. | MR | Zbl

[9] I. Babuška, M. Suri, The treatment of nonhomogeneous Dirichlet boundar conditions by the p-version of the finite element method, Num. Math. 55 (1989) 97-121. | MR | Zbl

[10] I. Babuška, M. Suri, The h-p version of the finite element method with quasi uniform meshes, RAIRO Modél. Math. Anal. Numér. 21 (1987) 199-238. | Numdam | MR | Zbl

[11] P. G. Clarlet, The finite element method for elliptic problems. North Holland Publishing Co, Amsterdam, 1987. | Zbl

[12] M. Costabel, E. P. Stephan, The normal derivative of the double layer potential on polygons and Galerkin approximation. Appl. Anal. 16 (1983) 205-228. | MR | Zbl

[13] M. Costabel, E. P. Stephan, The method of Mellin transformation for boundary integral equations on curves with corners, Numerical Solutions of Singular Intégral Equations (ed. A. Gerasoulis, R. Vichnevetsky) IMACS (1984) 95-102.

[14] M. Costabel, E. P. Stephan, Boundary integral equations for mixed boundary value problems in polygonal domains and Galerkin approximations, in : Mathematical Models and Methods in Mechanics(1981), W. Fiszdon and K. Wilmânski, editors, Banach Center Publications, Vol. 5, 15, pp. 175-251, PWN-Polish Scientific Publishers, Warsaw (1985). | MR | Zbl

[15] M. R. Dorr, The approximation theory for the p-version of the finite element method. SIAM J. Numer. Anal. 21 (1984) 1180-1207. | MR | Zbl

[16] W. Gui, I. Babuška, he h-p versions of the finite element method in one dimension. Parts 1-3, Numer. Math. 49 (1986) 577-683. | MR

[17] S. Hildebrandt, E. Wlenholtz, Constructive proofs of representation theorems in separable Hilbert space, Comm. Pure Appl. Math. 17 (1964) 369-373. | MR | Zbl

[18] J. L. Lions, E. Magenes, Non-Homogeneous Boundary Value Problems and Applications I, Springer-Verlag, Berlin, Heidelberg, New York, 1972. | Zbl

[19] T. Von Petersdorff, Boundary value problems of elasticity in polyhedra-Singularities and approximation by boundary elements, Ph. D. Thesis, TH Darmstadt (1989).

[20] E. Rank, Adaptive Boundary Element Methods, in : Boundary Elements 9, Vol. 1 (ed C A. Brebbia, W. L. Wendland, G. Kuhn), Springer-Verlag, Heidelberg (1987) 259-273. | MR

[21] E. P. Stephan, M. Suri, On the convergence of the p-version of the boundary element Galerkin method, Math. Comp. 52 (1989) 31-48. | MR | Zbl

[22] E. P. Stephan, W. L. Wendland, Remarks to Galerkin and least squaresmethods with finite elements for general elliptic problem. Manuscripta Geodaetica 1 (1976) 93-123. | Zbl

[23] E. P. Stephan, W. L. Wendland, An augmented Galerkin procedure for the boundary integral method applied to two-dimensional screen and crack problems. Appl. Anal. 18 (1984) 183-219. | MR | Zbl

[24] E. P. Stephan, W. L. Wendland, A hypersingular boundary integral method for two-dimensional screen and crack problem, Arch. Rational Mech. Anal. 112 (1990) 363-390. | MR | Zbl

[25] H. Triebel, Interpolation Theory, Function Space, Differential Operators. North-Holland Publishing Co., Amsterdam, 1987. | MR | Zbl

[26] W. L. Wendland, On some mathematical aspects of boundary element methods for elliptic problems, in : J. Whiteman, editor, Mathematics of Finite Elements and Applications V, pp. 193-227, Academic press, London, 1985. | MR | Zbl

[27] W. L. Wendland, Splines versus trigonometrie polynomials, h-versus p-version in 2D boundary integral methods. In D. Griffïths, R. Mitchell eds., Dundee Biennial Conference on Numerical Analysis, 1985. 25, n° 6, 1991. | Zbl