Literatur [1] Adams, R. A.: Sobolev Spaces. Academic Press, New York, London, 1975. [2] Axelsson, 0.: Iterative Solution Methods. Cambridge University Press, Cam- bridge, 1994. [3] Axelsson, 0., Barker, V. A.: Finite Element Solution of Boundary Value Problems: Theory and Computation. Academic Press, Orlando, 1984. [4] Aziz, A., Babuska, 1.: On the angle condition in the finite element method. SIAM J. Numer. Anal. 13 (1976) 214-226. [5] Babuska, I.: The finite element method with Lagrangian multipliers. Numer. Math. 20 (1973) 179-192. [6] Barrett, R. et al.: Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods. SIAM, Philadelphia, 1993. [7] Bebendorf, M.: Effiziente numerische Losung von Randintegralgleichungen unter Verwendung von Niedrigrang-Matrizen. Dissertation, Universitat des Saarlandes, Saarbriicken, 2000. [8] Bebendorf, M.: Approximation of boundary element matrices. Numer. Math. 86 (2000) 565-589. [9] Bebendorf, M., Rjasanow, S.: Adaptive low-rank approximation of colloca- tion matrices. Computing 70 (2003) 1-24. [10] Bergh, J., Lofstrom, J.: Interpolation Spaces. An Introduction. Springer, Berlin, New York, 1976. [11] Bjl1lrstad, P., Gropp, W., Smith, B.: Domain Decomposition. Parallel Multile- vel Methods for Elliptic Partial Differential Equations. Cambridge University Press, 1996. [12] Braess, D.: Finite Elemente. Springer, Berlin, 1991. [13] Bramble, J. H.: The Lagrange multiplier method for Dirichlet's problem. Math. Compo 37 (1981) 1-11.
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Literatur
[1] Adams, R. A.: Sobolev Spaces. Academic Press, New York, London, 1975.
[3] Axelsson, 0., Barker, V. A.: Finite Element Solution of Boundary Value Problems: Theory and Computation. Academic Press, Orlando, 1984.
[4] Aziz, A., Babuska, 1.: On the angle condition in the finite element method. SIAM J. Numer. Anal. 13 (1976) 214-226.
[5] Babuska, I.: The finite element method with Lagrangian multipliers. Numer. Math. 20 (1973) 179-192.
[6] Barrett, R. et al.: Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods. SIAM, Philadelphia, 1993.
[7] Bebendorf, M.: Effiziente numerische Losung von Randintegralgleichungen unter Verwendung von Niedrigrang-Matrizen. Dissertation, Universitat des Saarlandes, Saarbriicken, 2000.
[8] Bebendorf, M.: Approximation of boundary element matrices. Numer. Math. 86 (2000) 565-589.
[9] Bebendorf, M., Rjasanow, S.: Adaptive low-rank approximation of collocation matrices. Computing 70 (2003) 1-24.
[10] Bergh, J., Lofstrom, J.: Interpolation Spaces. An Introduction. Springer, Berlin, New York, 1976.
[11] Bjl1lrstad, P., Gropp, W., Smith, B.: Domain Decomposition. Parallel Multilevel Methods for Elliptic Partial Differential Equations. Cambridge University Press, 1996.
[13] Bramble, J. H.: The Lagrange multiplier method for Dirichlet's problem. Math. Compo 37 (1981) 1-11.
354 Literatur
[14] Bramble, J. H., Pasciak, J. E.: A preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems. Math. Compo 50 (1988) 1-17.
[15] Bramble, J. H., Pasciak, J. E., Steinbach, 0.: On the stability of the 12 projection in Hl(O). Math. Compo 71 (2002) 147-156.
[16] Bramble, J. H., Pasciak, J. E., Xu, J.: Parallel multilevel preconditioners. Math. Compo 55 (1990) 1-22.
[17] Bramble, J. H., Zlamal, M.: Triangular elements in the finite element method. Math. Compo 24 (1970) 809-820.
[18] Brenner, S., Scott, R. L.: The Mathematical Theory of Finite Element Methods. Springer, New York, 1994.
[19] Breuer, J.: Wavelet-Approximation der symmetrischen VariationsformuHerung von Randintegralgleichungen. Diplomarbeit, Mathematisches Institut A, Universitat Stuttgart, 2001.
[20] Carstensen, C., Kuhn, M., Langer, U.: Fast parallel solvers for symmetric boundary element domain decomposition methods. Numer. Math. 79 (1998) 321-347.
[21] Ciarlet, P. G.: The Finite Element Method for Elliptic Problems. NorthHolland, 1978.
[22] Clement, P.: Approximation by finite element functions using local regularization. RAIRO Anal. Numer. R-2 (1975) 77-84.
[23] Costabel, M.: Symmetric methods for the coupling of finite elements and boundary elements. In: Boundary Elements IX (C. A. Brebbia, G. Kuhn, W. L. Wendland eds.), Springer, Berlin, pp. 411-420, 1987.
[24] Costabel, M.: Boundary integral operators on Lipschitz domains: Elementary results. SIAM J. Math. Anal. 19 (1988) 613-626.
[25] Costabel, M., Stephan, E. P.: Boundary integral equations for mixed boundary value problems in polygonal domains and Galerkin approximations. In: Mathematical Models and Methods in Mechanics. Banach Centre Publ. 15, PWN, Warschau, pp. 175-251, 1985.
[26] Dahmen, W., ProBdorf, S., Schneider, R.: Wavelet approximation methods for pseudodifferential equations I: Stability and convergence. Math. Z. 215 (1994) 583-620.
Literatur 355
[27] Dahmen, W., Prof3dorf, S., Schneider, R: Wavelet approximation methods for pseudodifferential equations II: Matrix compression and fast solution. Adv. Comput. Math. 1 (1993) 259-335.
[28] Dautray, R, Lions, J. L.: Mathematical Analysis and Numerical Methods for Science and Technology. Volume 4: Integral Equations and Numerical Methods. Springer, Berlin, 1990.
[29] Duvaut, G., Lions, J. L.: Inequalities in Mechanics and Physics. Springer, Berlin, 1976.
[30] Fix, G. J., Strang, G.: An Analysis of the Finite Element Method. Prentice Hall Inc., Englewood Cliffs, 1973.
[31] Fortin, M.: An analysis of the convergence of mixed finite element methods. RA.I.RO. Anal. Numer. 11 (1977) 341-354.
[32] Fox, L., Huskey, H. D., Wilkinson, J. H.: Notes on the solution of algebraic linear simultaneous equations. Quart. J. Mech. Appl. Math. 1 (1948) 149-173.
[33] Giebermann, K.: Schnelle Summationsverfahren zur numerischen Losung von Integralgleichungen fur Streuprobleme im JR3. Dissertation, Universitat Karlsruhe, 1997.
[34] Gradshteyn, I. S., Ryzhik, I. M.: Table of Integrals, Series, and Products. Academic Press, New York, 1980.
[35] Greengard, L.: The Rapid Evaluation of Potential Fields in Particle Systems. The MIT Press, Cambridge, MA, 1987.
[36] Greengard, L., Rokhlin, V.: A fast algorithm for particle simulations. J. Comput. Phys. 73 (1987) 325-348.
[38] Haase, G.: Parallelisierung numerischer Algorithmen fur partielle Differentialgleichungen. B. G. Teubner, Stuttgart, Leipzig, 1999.
[39] Hackbusch, W.: Iterative Losung grof3er schwachbesetzter Gleichungssysteme. B. G. Teubner, Stuttgart, 1993.
[40] Hackbusch, W.: Theorie und Numerik elliptischer Differentialgleichungen. B. G. Teubner, Stuttgart, 1996.
[41] Hackbusch, W.: A sparse matrix arithmetic based on 1i-matrices. I. Introduction to 1i-matrices. Computing 62 (1999) 89-108.
356 Literatur
[42] Hackbusch, W., Nowak, Z. P.: On the fast matrix multiplication in the boundary element method by panel clustering. Numer. Math. 54, 463-491 (1989).
[43] Boundary Elements: Implementation and Analysis of Advanced Algorithms. Notes on Numerical Fluid Mechanics 54, Vieweg, Braunschweig, 1996.
[44] Han, H.: The boundary integro-differential equations of three-dimensional Neumann problem in linear elasticity. Numer. Math. 68 (1994) 269-281.
[45] Harbrecht, H.: Wavelet Galerkin schemes for the boundary element method in three dimensions. Dissertation, TU Chemnitz, 2001.
[46] Hestenes, M., Stiefel, E.: Methods of conjugate gradients for solving linear systems. J. Res. Nat. Bur. Stand 49 (1952) 409-436.
[47] Hormander, L.: The Analysis of Linear Partial Differential Operators I, Springer, Berlin, 1983.
[48] Hsiao, G. C., Stephan, E. P., Wendland, W. L.: On the integral equation method for the plane mixed boundary value problem of the Laplacian. Math. Meth. Appl. Sci. 1 (1979) 265-321.
[49] Hsiao, G. C., Wendland, W. L.: A finite element method for some integral equations of the first kind. J. Math. Anal. Appl. 58 (1977) 449-481.
[50] Jung, M., Langer, U.: Methode der finiten Elemente fur Ingenieure. B. G. Teubner, Stuttgart, Leipzig, Wiesbaden, 2001.
[51] Jung, M., Steinbach, 0.: A finite element-boundary element algorithm for inhomogeneous boundary value problems. Computing 68 (2002) 1-17.
[52] Kupradze, V. D.: Three-dimensional problems of the mathematical theory of elasticity and thermoelasticity. North-Holland, Amsterdam, 1979.
[53] Kythe, P. K.: Fundamental Solutions for Differential Operators and Applications. Birkhauser, Boston, 1996.
[54] Ladyzenskaja, O. A.: Funktionalanalytische Untersuchungen der NavierStokesschen Gleichungen. Akademie-Verlag, Berlin, 1965.
[55] Ladyzenskaja, O. A., Ural'ceva, N. N.: Linear and quasilinear elliptic equations. Academic Press, New York, 1968.
[56] Lage, C., Schwab, C.: Wavelet Galerkin algorithms for boundary integral equations. SIAM J. Sci. Comput. 20 (1999) 2195-2222.
[57] U. Langer, Parallel iterative solution of symmetric coupled fe/be equations via domain decomposition. Contemp. Math. 157 (1994) 335-344.
Literatur 357
[58] Maue, A. W.: Zur Formulierung eines allgemeinen Beugungsproblems durch eine Integralgleichung. Z. f. Physik 126 (1949) 601-618.
[59] McLean, W.: Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press, 2000.
[60] McLean, W., Steinbach, 0.: Boundary element preconditioners for a hypersingular boundary integral equation on an intervall. Adv. Comput. Math. 11 (1999) 271-286.
[61] McLean, W., Tran, T.: A preconditioning strategy for boundary element Galerkin methods. Numer. Meth. Part. Diff. Eq. 13 (1997) 283-30l.
[62] Necas, J.: Les Methodes Directes en Theorie des Equations Elliptiques. Masson, Paris und Academia, Prag, 1967.
[63] Nedelec, J. C.: Integral equations with non integrable kernels. Int. Eq. Operator Th. 5 (1982) 562-572.
[64] Of, G.: Die Multipolmethode fur Randintegralgleichungen. Diplomarbeit, Mathematisches Institut A, Universitat Stuttgart, 200l.
[65] Of, G., Steinbach, 0.: A fast multipole boundary element method for a modified hypersingular boundary integral equation. In: Analysis and Simulation of Multifield Problems (W. L. Wendland, M. Efendiev eds.), Lecture Notes in Applied and Computational Mechanics 12, Springer, Heidelberg, 2003, pp. 163-169.
[67] ProBdorf, S., Silbermann, B.: Numerical Analysis for Integral and Related Operator Equations. Birkhauser, Basel, 1991.
[68] Quarteroni, A., Valli, A.: Domain Decomposition Methods for Partial Differential Equations. Oxford Science Publications, 1999.
[69] Reidinger, B., Steinbach, 0.: A symmetric boundary element method for the Stokes problem in multiple connected domains. Math. Meth. Appl. Sci. 26 (1993) 77-93.
[70] Rudin, W.: Functional Analysis. McGraw-Hill, New York, 1973.
[71J Saad, Y., Schultz, M. H.: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7 (1985) 856-869.
[73] Sauter, S. A.: Variable order panel clustering. Computing 64 (2000) 223-261.
[74] Schatz, A. H., Thomee, V., Wendland, W. L.: Mathematical Theory of Finite and Boundary Element Methods. Birkhauser, Basel, 1990.
[75] Schneider, R.: Multiskalen- und Wavelet-Matrixkompression: Analysisbasierte Methoden zur effizienten Losung groBer vollbesetzter Gleichungssysteme. Advances in Numerical Mathematics. B. G. Teubner, Stuttgart, 1998.
[76] Schwab, C.: p- and hp-Finite Element Methods. Theory and Applications in Solid and Fluid Mechanics. Clarendon Press, Oxford, 1998.
[77] Scott, L. R., Zhang, S.: Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Compo 54 (1990) 483-493.
[78] Steinbach, 0.: Fast evaluation of Newton potentials in boundary element methods. East-West J. Numer. Math. 7 (1999) 211-222.
[79] Steinbach, 0.: On the stability of the L2 projection in fractional Sobolev spaces. Numer. Math. 88 (2001) 367-379.
[80] Steinbach, 0.: On a generalized L2 projection and some related stability estimates in Sobolev spaces. Numer. Math. 90 (2002) 775-786.
[81] Steinbach, 0.: Stability estimates for hybrid coupled domain decomposition methods. Lecture Notes in Mathematics 1809, Springer, Heidelberg, 2003.
[82] Steinbach, 0., Wendland, W L.: The construction of some efficient preconditioners in the boundary element method. Adv. Comput. Math. 9 (1998) 191-216.
[83] Steinbach, 0., Wendland, W. L.: On C. Neumann's method for second order elliptic systems in domains with non-smooth boundaries. J. Math. Anal. Appl. 262 (2001) 733-748.
[84] Triebel, H.: Hohere Analysis. Verlag Harri Deutsch, Frankfurt/M., 1980.
[85] Tyrtyshnikov, E. E.: Mosaic-skeleton approximations. Calcolo 33 (1996) 47-57.
[86] Verchota, G.: Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains. J. Funct. Anal. 59 (1984) 572-611.
[87] Vladimirov, V. S.: Equations of Mathematical Physics. Marcel Dekker, New York, 1971.
Literatur 359
[88J van der Vorst, H. A.: Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 13 (1992) 631-644.
[89J Walter, W.: Einfuhrung in die Theorie der Distributionen. BI Wissenschaftsverlag, Mannheim, 1994.
[90J Wendland, W. L.: Elliptic Systems in the Plane. Pitman, London, 1979.
[91J Wendland, W. L.: Boundary Element Topics. Springer, Heidelberg, 1997.
[92J Wendland, W. L., Zhu, J.: The boundary element method for three-dimensional Stokes flow exterior to an open surface. Mathematical and Computer Modelling 15 (1991) 19-42.
[93J Wloka, J.: Funktionalanalysis und Anwendungen. Walter de Gruyter, Berlin, 1971.
[94] Wloka, J.: Partielle Differentialgleichungen. B. G. Teubner, Stuttgart, 1982.
[95] Xu, J.: An introduction to multilevel methods. In: Wavelets, multilevel methods and elliptic PDEs. Numer. Math. Sci. Comput., Oxford University Press, New York, 1997, pp. 213-302.