Dietrich Braess' Reports

Books and Updates Some Reprints Recent Papers

Books: Corrections and Updates

Approximationstheorie. Vorlesungstext für die Fernuniversität Hagen (deutsch). 480 S. 1979
Advances in Multigrid Methods. D. Braess, W. Hackbusch, and U. Trottenberg, Eds. Vieweg, Braunschweig-Wiesbaden 1985
Nonlinear Approximation Theory. Springer-Verlag, Berlin-Heidelberg-New York 1986
Numerical Methods in Approximation Theory. D. Braess and L.L. Schumaker, Eds. Birkhäuser-Verlag, Basel 1992
Finite Elemente: Theorie, schnelle Löser und Anwendungen in der Elastizitätstheorie. Springer-Verlag, Berlin-Heidelberg-New York 1992, 1997, 2003, 2007
Korrekturen und Ergänzungen zu den Ausgaben von 2003 and 1997
Finite Elements: Theory, Fast Solvers and Applications in Solid Mechanics. Cambridge University Press, Cambridge, 1997, 2001, 2007. - ISBN: 0 521 70518-9
What are the specialties and highlights ?
Corrections and extensions to the editions 2007 and 2001.

Solutions of selected problems from the English editions 2001 and 2007
The collection of solutions will be enlarged on request.

Some Reprints - Complete list of publications
Click on the number for getting a ps or pdf file

14 Über ein Paradoxon aus der Verkehrsplanung. Unternehmensforschung 12, 258-268 (1968) [English: A paradox of traffic planning; cf. 114] more information
81 Uniform convergence of mixed interpolated elements for Reissner-Mindlin plates (joint paper with P. Peisker). M²AN (RAIRO) 26, 557-574 (1992)
86 Finite elements for Kirchhoff and Mindlin-Reissner plates. In "Advances in Computational Mathematics" (H.P. Dikshit and C. Micchelli, eds.), pp. 1-13, World Scientific Publishing Co. 1994
88 Asymptotics for the approximation of wave functions by exponential sums. J. Approximation Theory 83, 93-103 (1995)
89 Towards algebraic multigrid for elliptic problems of second order. Computing 55, 379-393 (1995)
92 Stability of Saddle Point Problems with Penalty. M²AN 30, 731-742 (1996)
93 An efficient smoother for the Stokes problem (joint paper with R. Sarazin). Applied Numerical Math. 23, 3-20 (1997) - including notes added after publication
94 Block SSOR preconditioners for 3D-groundwater flow problems (joint paper with C. König). in "Modeling and Computation in Environmental Sciences" (R. Helmig et al, eds.), pp. 86-90. Vieweg, Braunschweig - Wiesbaden 1997
96 Stability estimates of the mortar finite element method for 3-dimensional problems (joint paper with W. Dahmen). East-West J. Numer. Math. 6(4), (1998), 249-264
97 Enhanced assumed strain elements and locking in membrane problems. Comput. Methods Appl. Mech. Engrg. 165, 155-174 (1998)
98 A class of equivalent enhanced assumed strain and hybrid stress finite elements (joint paper with M. Bischoff and E. Ramm). Comput. Mechanics 22, 443-449 (1999)
99 A cascadic multigrid algorithm for the Stokes equations (joint paper with W. Dahmen). Numer. Math. 82, 179-191 (1999) - The ideas in 106 are useful for getting an efficient implementation of the algorithm; see also the notes added after publication that you get with the download of 93.
100 Multigrid method for nonconforming FE-discretisations with application to nonmatching grids (joint paper with M. Dryja and W. Hackbusch). Computing 63, 1-25 (1999)
101 A multigrid algorithm for the mortar finite element method (joint paper with W. Dahmen and C. Wieners). SIAM J. Numer. Anal. 37, 48-69 (2000) - The correspondence of the saddle point formulation here with the theory of nonconforming methods is discussed in 104.
102 Approximation on simplices with respect to weighted Sobolev norms (joint paper with C. Schwab). J. Approximation Theory 103, 329-337 (2000) - More about the context and a larger number of citations are fond in 114.
103 Note on the approximation of powers of the distance in 2-dimensional domains. Constructive Approximation 17, 147-151 (2001)
The extension to d-space with d grater than 2 has been described more recently.
104 Analysis of a multigrid algorithm for the mortar finite element method. In "Domain Decomposition Methods in Science and Engineering", Proceedings of DD12 (T. Chan, T. Kako, H. Kawarada and O. Pironneau, eds.), pp. 1-13, Chiba, 2001
105 Enhanced assumed strain elements and nearly incompressible material. 2nd European Conference on Computational Mechanics, Krakau, June 2001 (available also on CD-ROM)
106 A cascadic multigrid method for mortar elements (joint paper with P. Deuflhard and K. Lipnikov). Computing 69, 205-225 (2002)
107 The mortar element method revisited - What are the right norms? (joint paper with W. Dahmen). In "Domain Decomposition Methods in Science and Engineering", Proceedings of DD13 (N. Debit, M. Garbey, R. Hoppe, D. Keyes, Y. Kuznetsov and J. Périaux, eds.) CIMNE, Barcelona 2002
108 How to achieve minimax expected Kullback-Leibler distance from an unknown finite distribution (joint paper with J. Forster, T. Sauer, and H.U. Simon). In "Algorithmic Learning Theory", Proceedings of the 13th International Conference ALT 2002" (N. Cesa-Bianchi, N. Numao, and R. Reischuk, eds.), pp. 380-394, Springer-Verlag, Heidelberg 2002
109 Uniform convergence and a posteriori error estimators for the enhanced strain finite element method (joint paper with C. Carstensen and B.D. Reddy). Numer. Math. 96, 461-479 (2004)
The impact of the results was emphasized in a talk in Bad Honnef, Sept. 2003: There is no locking in the deformations and in the strains, but there may be still locking in the volume term of the stresses. The latter is concealed since there are no checkerboard modes.
An extended abstract (3 pages) of a talk in Oberwolfach with a quick review of the a priori estimate is also available.
110 A cascadic multigrid algorithm for variational inequalities (joint paper with H. Blum and F.T. Suttmeier). Computing and Visualization in Science 7, 153-157 (2004)
111 Bernstein polynomials and learning theory (joint paper with T. Sauer). J. Approximation Theory 128, 187-206 (2004). PDF
112 The asymptotic minimax risk for the estimation of constrained binomial and multinomial probabilities (joint paper with H. Dette). Sankhyā 66, 707-732 (2004). PDF
113 A finite element method for nearly incompressible elasticity problems (joint paper with Pingbing Ming). Math. Comp. 74, 25-52 (2005)
114 On a paradox of traffic planning. (joint translation of 14 with Anna Nagurney, Tina Wakolbinger) Transportation Science 39, 446-450 (2005) more information
115 Approximation on simplices and orthogonal polynomials. In "Trends and Applications in Constructive Approximation" (M.G. de Bruin, D.H. Mache and J. Szabados, eds.), pp. 53-60. Birkhäuser Verlag, Basel 2005 PDF
116 Approximation of 1/x by exponential sums in [1,∞) (joint paper with W. Hackbusch). IMA J. Numer. Anal. 25, 685-697 (2005)
117 A posteriori error estimators for obstacle problems - Another look. Numer. Math. 101, 415-421 (2005)
118 Improvements for some condition number estimates for preconditioned system in p-FEM (joint paper with S. Beuchler). Numer. Lin. Algebra Appl. 13, 573-588 (2006)
119 On the number of support points of maximin and Bayesian optimal designs (joint paper with H. Dette). The Annals of Statistics 35, 772-792 (2007) PDF
120 Convergence analysis of a conforming adaptive finite element method for an obstacle problem (joint paper with C. Carstensen and R. Hoppe). Numer. Math. 107, 455-471 (2007)
A brief introduction into the papers no. 121, 123, 124, and 126 can be found in a research report
121 Equilibrated residual error estimator for edge elements (joint paper with J. Schöberl). Math. Comp. 77, 651-672 (2008)
122 Efficient 3D-finite-element-formulation for thin mechanical and piezoelectric structures. (joint paper with M. Kaltenbacher). Int. J. Numer. Methods Engrg. 73, 147-161 (2008)
123 A posteriori estimators for obstacle problems by the hypercircle method (joint paper with R.H.W. Hoppe and J. Schöberl). Comp. Visual. Sci. 11, 351-362 (2008)
124 Equilibrated residual error estimates are p-robust (joint paper with V. Pillwein and J. Schöberl). Comput. Methods Appl. Mech. Engrg. 198, 1189–1197 (2009)
125 An a posteriori error estimate and a comparison theorem for the nonconforming P₁ element. Calcolo 46, 149-156 (2009) [typos corrected in 2010]
126 Error reduction in adaptive finite element approximations of elliptic obstacle problems (joint paper with C. Carstensen and R. Hoppe). J. Computational Mathematics 27, 170-183 (2009)
127 On the efficient eomputation of high-dimensional integrals and the approximation by exponential sums (joint paper with W. Hackbusch). In "Multiscale, Nonlinear and Adaptive Approximation", (R. A. DeVore and A. Kunoth, eds.), pp. 39-74. Springer-Verlag, Heidelberg 2009.
128 Shear locking in a plane elasticity problem and the enhanced strain method (joint paper with P. Ming and Z. Shi). SIAM J. Numer. Anal. 47, 4473-4491 (2010)