Schriftenverzeichnis DB

List of Publications

Dietrich Braess

Postscript or pdf files of papers marked by a full circle are available. Click on the number.

1. Die Konstruktion monotoner Iterationsfolgen zur Lösungseinschließung bei linearen Gleichungssystemen. Arch. Rational Mech. Anal. 9, 97-106 (1962)
2. Monotone Iterationsfolgen bei Gleichungssystemen mit fehlerhaften Koeffizienten und Iterationsbeschleunigung. Numer. Math. 7, 32-44 (1965)
3. Die Berechnung der Fehlergrenzen bei linearen Gleichungssystemen mit fehlerhaften Koeffizienten. Arch. Rational Mech. Anal. 19, 74-80 (1965)
4. Über Dämpfung bei Minimalisierungsverfahren. Computing 1, 264-272 (1966)
5. (gemeinsam mit H. Späth) Maßnahmen zur globalen Konvergenzerzwingung beim Newton'schen Verfahren für spezielle nichtlineare Gleichungssysteme. ZAMM 47, 409-410 (1967)
6. Einfluß der Wechselwirkung im Endzustand auf die Elektrospaltung des Deuterons in der Nähe der Schwelle. Z. Physik 184, 241-270 (1965)
7. (joint paper with G. Kramer) Inelastic electron-deuteron scattering with final-state interactions. Z. Physik 189, 242-268 (1966), desgl. in Proc. International Symposium on Electron and Photon Iteractions at High Energies 1965
8. (joint paper with D. Hasselmann and G. Kramer) Low momentum transfer neutron form factors from analysis of deuteron electrodisintegration. Z. Physik 198, 527-537 (1967)
9. (joint paper with G. Fröhlich, A. Jansen, H. Küsters and K. Schröter) The calculation of fast power reactors. Proc. Conference of Fast Reactors in London 1966
10. (joint paper with K. Thurnay) Analyse von zweiten Exkursionen bei negativen Dopplerkoeffizienten. Bericht KFK 813 des Kernforschungszentrums Karlsruhe 1968
11. (joint paper with H. Küsters and K. Thurnay) Improvement of second excursion calculations. Proc. Conference on Safety of Fast Reactors in Aix-en-Provence 1967
12. Approximation mit Exponentialsummen. Computing 2, 309-321 (1967)
13. (joint paper with H. Werner) Über den Zusammenhang von Interpolation und diskreter T-Approximation mit rationalen Funktionen. Numer. Math. 13, 112-128 (1969)
14. Über ein Paradoxon aus der Verkehrsplanung. Unternehmensforschung 12, 258-268 (1968)
[English: A paradox of traffic planning; cf. 114] more information
15. Eine Möglichkeit zur Konvergenzbeschleunigung für bestimmte nichtlineare Probleme. Numer. Math. 14, 468-475 (1970)
16. Über die Vorzeichenstruktur der Exponentialsummen. J. Approximation Theory 3, 101-113 (1970)
17. Die Konstruktion der Tschebyscheff-Approximierenden bei der Anpassung mit Exponentialsummen. J. Approximation Theory 3, 261-273 (1970)
18. (joint paper with R. Schaback) Eine Lösungsmethode für die lineare Tschebyscheff-Approximation bei nicht erfüllter Haarscher Bedingung. Computing 6, 289-294 (1970)
19. Chebyshev approximation by spline functions with free knots. Numer. Math. 17, 357-366 (1971)
20. Die Bestimmung kürzester Pfade in Graphen und passende Datenstrukturen. Computing 8, 171-181 (1971)
21. On topological properties of sets admitting varisolvent functions. Proc. Amer. Math. Soc. 34, 453-456 (1972)
22. Über die Mehrdeutigkeit bei der Approximation durch Spline-Funktionen mit freien Knoten. ISNM 16, 9-18 (1972)
23. Chebyshev approximation by γ-polynomials. J. Approximation Theory 9, 20-43 (1973)
24. On a paper of C.B. Dunham concerning degeneracy in mean non-linear approximation. J. Approximation Theory 9, 313-315 (1973)
25. Chebyshev approximation by exponentials on finite subsets. Math. Comp. 27, 327-331 (1973)
26. A computational method for the non-linear transportation problem. OR-Verfahren 16, 57-67 (1973)
27. (joint paper with K.P. Hadeler) Simultaneous inclusion of the zeros of a polynomial. Numer. Math. 21, 161-165 (1973)
28. Global analysis and Chebyshev approximation by exponentials. In "Approximation Theory" (G.G. Lorentz, ed.) pp. 277-283. Academic Press 1973
29. Kritische Punkte bei der nichtlinearen Tschebyscheff-Approximation. Math. Z. 132, 327-341 (1973)
30. (joint paper with H. Werner) Tschebyscheff-Approximation mit einer Klasse rationaler Splinefunktionen II. J. Approximation Theory 10, 379-399 (1974)
31. Chebyshev approximation by γ-polynomials II. J. Approximation Theory 11, 16-37 (1974)
32. Geometrical characterizations for nonlinear uniform approximation. J. Approximation Theory 11, 260-274 (1974)
33. Morse-Theorie für berandete Mannigfaltigkeiten. Math. Ann. 208, 133-148 (1974)
34. Rationale Interpolation, Normalität und Monosplines. Numer. Math. 22, 219-232 (1974)
35. On the nonuniqueness of monosplines with least L₂-Norm. J. Approximation Theory 12, 91-93 (1974)
36. SQUFIT (Square-Fit) ein Programm zur nichtlinearen Anpassung von Meßdaten nach der Methode der kleinsten Quadrate. Schriftenreihe des Rechenzentrums der Universität Münster Nr. 6, 14 S. 1974
37. On varysolvency and alternation. J. Approximation Theory 12, 230-233 (1974)
38. (joint paper with M.P. Carroll) On uniqueness of L₁-approximation for certain families of spline functions. J. Approximation Theory 12, 362-364 (1974)
39. On the number of best approximations in certain nonlinear families of functions. Aequationes math. 12, 184-199 (1975)
40. On the degree of approximation by spline functions with free knots. Aequationes math. 12, 80-81 (1975)
41. An n-parameter Chebyshev set which is not a sun. Canad. Math. Bull. 18, 489-492 (1975)
42. Anregungen aus dem Schnittebenenalgorithmus für die Lösung des allgemeinen Transportproblems. Computing 15, 157-167 (1975)
43. (joint paper with J. Brink-Spalink and R. Schaback) Eine Bibliographie über nichtlineare Approximation. Schriftenreihe der Universität Bonn, Sonderforschungsbereich 72, 1975
44. Über das Anzahlproblem bei der rationalen L₂-Approximation. ISNM 26, 109-121 (1976)
45. On rational L₂-approximation. J. Approximation Theory 18, 136-151 (1976)
46. Nonlinear approximation. In "Approximation Theory II" (G.G. Lorentz, C.K. Chui and L.L. Schumaker, eds.) pp. 49-78. Academic Press 1976
47. Zur numerischen Stabilität des Newton-Verfahrens bei der nichtlinearen Tschebyscheff-Approximation. In "Approximation Theory, Bonn 1976" (R. Schaback und K. Scherer, eds.) pp. 54-62. Springer-Verlag 1976
48. Analysis of decay processes and approximation by exponentials. In "Optimal Estimation in Approximation" (C.A. Micchelli and T.J. Rivlin, eds.) pp. 257-266. Plenum Press 1977
49. Über die Einzugsbereiche der Nullstellen von Polynomen beim Newton-Verfahren. Numer. Math. 29, 123-132 (1977)
Le traduction en Français etait fait de P.J. Laurent, et l'auteur peut l'envoir une photocopie.
50. Chebyshev approximation by γ-polynomials III. On the number of solutions. J. Approximation Theory 24, 119-145 (1978)
51. (joint paper with G. Koch) On the existence of equilibria in asymmetrical multiclass-user transportation networks. Transportation Sci. 13, 56-63 (1979)
51a. "Approximationstheorie". Vorlesungstext für die Fernuniversität Hagen, 480 S. Text und 120 S. Begleitmaterial, 1979
52. Über die numerische Behandlung von Problemen mit kleinen Nennern. In "Numerische Methoden der Approximationstheorie Band 5" (Hrsg.: L. Collatz, G. Meinardus und H. Werner) ISNM 52, S. 49-68. Birkhäuser 1980
53. (joint paper with H.-P. Blatt) Zur rationalen Approximation von e^x auf [0,∞). J. Approximation Theory 30, 169-172 (1980)
54. Global analysis in nonlinear approximation and its application to exponential approximation. Part I: The uniqueness theorem for Haar embedded manifolds. Part II: Applications to exponential approximation. In "Approximation Theory and Applications" (Z. Ziegler, ed.) pp. 23-37 and S. 39-63. Academic Press 1981
55. The contraction number of a multigrid method for solving the Poisson equation. Numer. Math. 37, 387-404 (1981)
56. (joint paper with E. Grebe) A numerical analysis of load-flow calculation methods. IEEE Trans. Power App. Systems. 100, 3642-3647 (1981)
57. (joint paper with G. Nürnberger) Nonuniqueness of best L_p-Approximation of generalized functions by splines with free knots. Numer. Functional Anal. Optim. 4, 199-209 (1981-1982)
58. On the conjecture of Meinardus on rational approximation to e^x. J. Approximation Theory 36, 317-320 (1982)
59. (joint paper with E. Zehnder) On the numerical treatment of small divisor problems. Numer. Math. 39, 269-292 (1982)
60. The convergence rate of a multigrid method with Gauß-Seidel relaxation for the Poisson equation. Math. Comp. 42, 505-519 (1984) und (als Vortrag) in "Multigrid Methods" (W. Hackbusch and U. Trottenberg, eds.) pp. 368-386. Springer-Verlag, Berlin-Heidelberg-New York 1982
61. (joint paper with N. Dyn) On the uniqueness of monsplines and perfect splines of least L₁ and L₂norm. J. Analyse Math. 41, 217-233 (1982) und (als Vortragsauszug) in "Approximation Theory IV" (C.K. Chui, L.L. Schumaker and J.D. Ward, eds.) pp. 375-380. Academic Press, New York-London 1983
62. On the numerical solution of the one-dimensional Stefan problem by Newton's method. IMA J. Numer. Anal. 3, 161-172 (1983)
63. (joint paper with W. Hackbusch) A new convergence proof for the multigrid method including the V-cycle. SIAM J. Numer. Anal. 20, 967-975 (1983)
64. Mehrgitterverfahren zur Lösung von Finite-Element-Gleichungen. In "Diskretisierungen in der Kontinuumsmechanik" (Hrsg.: E. Stein und H. Werner) Bonn 1983
65. On the conjecture of Meinardus on rational approximation to e^x. II. J. Approximation Theory 40, 375-379 (1984)
66. On rational approximation of the exponential and the square root function. In "Rational Approximation and Interpolation" (P.R. Graves-Morris, E.B. Saff and R.S. Varga, eds.) pp. 89-99. Springer-Verlag, Berlin-Heidelberg-New York 1984
66a. (with W. Hackbusch and U. Trottenberg, eds.) "Advances in Multigrid Methods". Vieweg, Braunschweig-Wiesbaden 1985
67. (joint paper with B. Bojanov and N. Dyn) Generalized Gaussian quadrature formulas. J. Approximation Theory 48, 335-353 (1986)
68. (joint paper with N. Dyn) On the uniqueness of generalized monosplines of least L_p-norm. Constr. Approx. 2, 79-99 (1986)
69. (joint paper with P. Peisker) On the numerical solution of the biharmonic equation and the role of squaring matrices for preconditioning. IMA J. Numer. Anal. 6, 393-404 (1986)
70. "Nonlinear Approximation Theory". 290 p. Springer-Verlag, Berlin-Heidelberg-New York 1986
71. On nonuniqueness in rational L_p-approximation. J. Approximation Theory 51, 68-70 (1987)
72. On the combination of the multigrid method and conjugate gradients. In "Multigrid Methods II" (W. Hackbusch and Trottenberg, eds.) pp. 52-64. Springer-Verlag, Berlin-Heidelberg-New York 1986
73. Rational approximation of Stieltjes functions by the Carathéodory-Fejér method. Constr. Approx. 3, 43-50 (1987)
74. (joint paper with P. Peisker) A conjugate gradient method and a multigrid algorithm for Morley's finite element approximation of the biharmonic equation. Numer. Math. 50, 567-586 (1987)
75. A multigrid method for the membrane problem. Computational Mechanics 3, 321-329 (1988)
75a. (joint paper with R. Schaback) Helmut Werner (Nachruf). Jber. d. Dt. Math.-Verein 89, 179-195 (1987)
76. (joint paper with G. Schmid) Comparison of fast equation solvers for groundwater flow problems. In "Groundwater Flow and Quality Modelling" (E. Custodio et al, eds.) pp. 173-188. Reidel 1988
77. (joint paper with R. Verfürth) Multi-Grid methods for nonconforming finite element methods. SIAM J. Numer. Anal. 27, 979-986 (1990)
78. (joint paper with C. Blömer) A multigrid method for a parameter dependent problem in solid mechanics. Numer. Math. 57, 747-761 (1990)
79. Kirchhoff- and Mindlin-Reissner plates: Combinations from the viewpoint of finite elements. In "Nonlinear Computational Mechanics - State of the Art" (P. Wriggers and W. Wagner, eds.) pp. 1-10. Springer-Verlag 1991
80. "Finite Elemente: Theorie, schnelle Löser und Anwendungen in der Elastizitätstheorie". 310 S. Springer-Verlag, Berlin-Heidelberg-New York 1992, [2. Auflage 1997, 3. Auflage 2003, 4. Auflage 2007, 5. Auflage 2013]
81. (joint paper with P. Peisker) Uniform convergence of mixed interpolated elements for Reissner-Mindlin plates. M²AN (RAIRO) 26, 557-574 (1992)
81a. (with L.L. Schumaker, eds.) "Numerical Methods in Approximation Theory". Birkhäuser-Verlag, Basel 1992
82. (joint paper with V.N. Rusak) Best polynomial and rational approximations of function classe in the integral metric. (Russisch) Dokl. Akad. Nauk Belarusi 36, no. 3-4, 205-208 (1992)
83. (joint paper with A. Pinkus) Interpolation by ridge functions. J. Approximation Theory 73, 218-236 (1993)
84. (joint paper with M. Biebighäuser, P. Grassberger and R. Leuverink) Multi-Grid methods for steady state diffusion in random media. J. Comput. Physics 107, 118-123 (1993)
85. (joint paper with D.S. Lubinsky and E.B. Saff) Behavior of alternation points in best rational approximation. Acta Applicandae Mathematicae 33, 195-210 (1993)
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
87. (joint paper with H.Laschefski, H. Haneke and N. K. Mitra) Numerical investigatation of radial jet reattachment flows. Int. J. Numer. Methods in Fluids 18, 629-646 (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)
90. (joint paper with O. Klaas, R. Niekamp, E. Stein and F. Wobschal) Error indicators for mixed finite elements in 2-dimensional linear elasticity. Comput. Methods Appl. Mech. Engrg. 127, 345-356 (1995)
91. (joint paper with R. Verfürth) A posteriori error estimators for the Raviart-Thomas element. SIAM J. Numer. Anal. 33, 2431-2444 (1996)
92. Stability of saddle point problems with penalty. M²AN 30, 731-742 (1996)
93. (joint paper with R. Sarazin) An efficient smoother for the Stokes problem. Applied Numerical Math. 23, 3-20 (1997)
94. (joint paper with C. König) Block SSOR preconditioners for 3D-groundwater flow problems in "Modeling and Computation in Environmental Sciences" (R. Helmig et al, eds.), pp. 86-90. Vieweg, Braunschweig - Wiesbaden 1997
95. "Finite Elements. Theory, Fast Solvers and Applications in Solid Mechanics". xvi+323 pp. Cambridge University Press 1997 [2nd edition 2001, 3rd edition 2007]
96. (joint paper with W. Dahmen) Stability estimates of the mortar finite element method for 3-dimensional problems. East-West J. Numer. Math. 6(4), 249-264 (1998)
97. Enhanced assumed strain elements and locking in membrane problems. Comput. Methods Appl. Mech. Engrg. 165, 155-174 (1998)
98. (joint paper with M. Bischoff and E. Ramm) A class of equivalent enhanced assumed strain and hybrid stress finite elements. Comput. Mechanics 22, 443-449 (1999)
99. (joint paper with W. Dahmen) A cascadic multigrid algorithm for the Stokes equation. Numer. Math. 82, 179-191 (1999)
100. (joint paper with M. Dryja and W. Hackbusch) A multigrid method for nonconforming FE-discretisations with application to nonmatching grids. Computing 63, 1-25 (1999)
101. (joint paper with W. Dahmen and C. Wieners) A multigrid algorithm for the mortar finite element method. SIAM J. Numer. Anal. 37, 48-69 (2000)
102. (joint paper with C. Schwab) Approximation on simplices with respect to weighted Sobolev norms. J. Approximation Theory 103, 329-337 (2000)
103. Note on the approximation of powers of the distance in 2-dimensional domains, Constructive Approximation 17, 147-151 (2001)
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. (joint paper with P. Deuflhard and K. Lipnikov) A cascadic multigrid method for mortar elements. Computing 69, 205-225 (2002)
107. (joint paper with W. Dahmen) The mortar element method revisited - What are the right norms? 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. (joint paper with C. Carstensen and B.D. Reddy) Uniform convergence and a posteriori error estimators for the enhanced strain finite element method. 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. (joint paper with H. Blum and F.T. Suttmeier) A cascadic multigrid algorithm for variational inequalities. Computing and Visualization in Science 7, 153-157 (2004)
111. (joint paper with T. Sauer) Bernstein polynomials and learning theory. J. Approximation Theory 128, 187-206 (2004)
112. (joint paper with H. Dette) The asymptotic minimax risk for the estimation of constrained binomial and multinomial probabilities. Sankhyā 66, 707-732 (2004)
113. (joint paper with Pingbing Ming) A finite element method for nearly incompressible elasticity problems. 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
116. (joint paper with W. Hackbusch) Approximation of 1/x by exponential sums in [1,∞). 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. (joint paper with S. Beuchler) Improvements for some condition number estimates for preconditioned system in p-FEM. Numer. Lin. Algebra Appl. 13, 573-588 (2006)
119. (joint paper with H. Dette) On the number of support points of maximin and Bayesian optimal designs. The Annals of Statistics 35, 772-792 (2007)
120. (joint paper with C. Carstensen and R. Hoppe) Convergence analysis of a conforming adaptive finite element method for an obstacle problem. 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. (joint paper with J. Schöberl) Equilibrated residual error estimator for edge elements. Math. Comp. 77, 651-672 (2008)
122. (joint paper with M. Kaltenbacher) Efficient 3D-finite-element-formulation for thin mechanical and piezoelectric structures. Int. J. Numer. Methods Engrg. 73, 147-161 (2008)
123. (joint paper with R.H.W. Hoppe and J. Schöberl) A posteriori estimators for obstacle problems by the hypercircle method. Comp. Visual. Sci. 11, 351-362 (2008)
124. (joint paper with V. Pillwein and J. Schöberl) Equilibrated residual error estimates are p-robust. 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 the postscript file in 2010]
126. (joint paper with C. Carstensen and R. Hoppe) Error reduction in adaptive finite element approximations of elliptic obstacle problems. J. Computational Mathematics 27, 170-183 (2009)
127. (joint paper with W. Hackbusch) On the efficient eomputation of high-dimensional integrals and the approximation by exponential sums. In "Multiscale, Nonlinear and Adaptive Approximation", (R. A. DeVore and A. Kunoth, eds.), pp. 39-74. Springer-Verlag, Heidelberg 2009.
128. (joint paper with P. Ming and Z. Shi) An error estimate for a plane elasticity problem and the enhanced strain method. SIAM J. Numer. Anal. 47, 4473-4491 (2010)
129. (joint paper with S. Sauter and C. Schwab) On the justification of plate models. J. Elasticity 103, 53-71 (2011)
130. (joint paper with H. Dette) Optimal discriminating designs for several competing regression models. The Annals of Statistics 41, 897-922 (2013)
131. (joint paper with T. Fraunholz and R. Hoppe) An equilibrated a posteriori error estimator for the interior penalty discontinuous Galerkin method. SIAM J. Numer. Anal. 52, 2121-2136 (2014)
132. (joint paper with R. Hoppe and C. Linsenmann) A two-energies principle for the biharmonic equation and an a posteriori error estimator for an Interior Penalty Discontinuous Galerkin approximation. ESAIM: M2AN 52, 2479-2504, (2019)
133. (joint paper with A.S. Pechstein and J. Schöberl) An equilibration-based a posteriori error bound for the biharmonic equation and two finite element methods. IMA J. Numer. Anal. 40, 951–975 (2020)

Feb. 14, 2023