The $h-p$ version of the boundary element method on polygonal domains with quasiuniform meshes

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1. [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. [2] E. ALARCON, A. REVERTER, J. MOLINA, Hierarchical boundary elements. Comput. and Structures, 20 (1985) 151-156. Zbl0581.73095
3. [3] E. ALARCON, A. REVERTER, p-adaptive boundary elements. Internat. J.Numer. Methods Engrg. 23 (1986) 801-829. Zbl0593.65068
4. [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. Zbl0731.73078MR1067939
5. [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. Zbl0268.65052MR421106
6. [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. Zbl0487.65058MR623044
7. [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. Zbl0709.65079
8. [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. Zbl0487.65059MR615529
9. [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. Zbl0673.65066MR987158
10. [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. Zbl0623.65113MR896241
11. [11] P. G. ClARLET, The finite element method for elliptic problems. North Holland Publishing Co, Amsterdam, 1987. Zbl0383.65058
12. [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. Zbl0508.31003MR712733
13. [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. [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). Zbl0655.65129MR874845
15. [15] M. R. DORR, The approximation theory for the p-version of the finite element method. SIAM J. Numer. Anal. 21 (1984) 1180-1207. Zbl0572.65074MR765514
16. [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. MR861522
17. [17] S. HILDEBRANDT, E. WlENHOLTZ, Constructive proofs of representation theorems in separable Hilbert space, Comm. Pure Appl. Math. 17 (1964) 369-373. Zbl0131.13401MR166608
18. [18] J. L. LIONS, E. MAGENES, Non-Homogeneous Boundary Value Problems and Applications I, Springer-Verlag, Berlin, Heidelberg, New York, 1972. Zbl0223.35039
19. [19] T. VON PETERSDORFF, Boundary value problems of elasticity in polyhedra-Singularities and approximation by boundary elements, Ph. D. Thesis, TH Darmstadt (1989). 
20. [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. MR965323
21. [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. Zbl0661.65118MR947469
22. [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. Zbl0353.65067
23. [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. Zbl0522.73083MR767500
24. [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. Zbl0725.73091MR1077265
25. [25] H. TRIEBEL, Interpolation Theory, Function Space, Differential Operators. North-Holland Publishing Co., Amsterdam, 1987. Zbl0387.46032MR503903
26. [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. Zbl0587.65079MR811035
27. [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. Zbl0653.65082

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