Prof. i.R. Dr. Rüdiger Verfürth

Contact: ruediger.verfuerth(at)rub.de

Contents

• Books
• Articles
• Conference Proceedings
• arXiv
• Reports
• Lecture Notes
• Handouts

Books

1. A Posteriori Error Estimation Techniques for Finite Element Methods.
   Oxford University Press, April 2013
   (416 pages, 33 b/w illustrations, 2 page colour plate section, ISBN 978-0-19-967942-3)
2. A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques.
   Wiley-Teubner, 1996 (150 pp)
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Journal Articles

1. (with C. Kreuzer and P. Zanotti) Quasi-Optimal and Pressure Robust Discretizations of the Stokes Equations by Moment- and Divergence-Preserving Operators
   CMAM 21, no. 2, pp. 423-443 (2020) (arXiv doi)
2. (with P. Zanotti) A Quasi-Optimal Crouzeix-Raviart Discretization of the Stokes Equations
   SIAM J. Numer. Anal. 57, no. 3, pp. 1082-1099 (2019) (arXiv)
3. A Posteriori Error Estimates for Non-Stationary Non-Linear Convection-Diffusion Equations
   Calcolo 55, art. 20 (2018) (online)
4. (with F. Tantardini and A. Veeser) Robust localization of the best error with finite elements in the reaction-diffusion norm.
   Constr. Approx. 42, no. 2, pp. 313-347 (2015)
5. (with L. Tobiska) Robust a posteriori error estimates for stabilized finite element methods.
   IMA J. Numer. Anal. 35, no. 4, pp. 1652-1671 (2015)
6. (with A. Veeser) Poincaré constants of finite element stars.
   IMA J. Numer. Anal. 32, no. 1, pp. 30-47 (2012)
7. (with C. Bernardi and F. Hecht) A posteriori error analysis of the method of characteristics.
   M3AS 21, no. 6, pp. 1355-1376 (2011)
8. A posteriori error analysis of space-time finite element discretizations of the time-dependent Stokes equations.
   Calcolo 47, no. 3, pp. 149-167 (2010)
9. A note on constant-free a posteriori error estimates.
   SIAM J. Numer. Anal. 47, no. 4, pp. 3180-3194 (2009)
10. (with C. Bernardi and F. Hecht) A finite element discretization of the three-dimensional Navier-Stokes equations with mixed boundary conditions.
    RAIRO M2AN 43, pp. 1185-1201 (2009)
11. (with A. Veeser) Explicit upper bounds for dual norms of residuals.
    SIAM J. Numer. Anal. 47, no. 3, pp. 2387-2405 (2009)
12. Robust a posteriori error estimates for non-stationary convection-diffusion equations.
    SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1783-1802 (2005)
13. Robust a posteriori error estimates for stationary convection-diffusion equations.
    SIAM J. Numer. Anal., Vol. 43, No. 4, pp. 1766-1782 (2005)
14. (with M. Lonsing) A posteriori error estimators for mixed finite element methods in linear elasticity.
    Numer. Math. 97, 757-778 (2004)
15. (with C. Bernardi) A posteriori error analysis of the fully discretized time-dependent Stokes equations.
    RAIRO M2AN 38, 437-455 (2004)
16. (with M. Lonsing) On the stability of BDMS and PEERS elements.
    Numer. Math. 99, 131-140 (2004)
17. (with A. Bergam and Z. Mghazli) Estimation a posteriori d'un schéma de volumes finis pour un problème non linéaire.
    Numer. Math. 95, 599 - 624 (2003)
18. A posteriori error estimates for finite element discretizations of the heat equation.
    Calcolo 40, 195 - 212 (2003)
19. (with M. Afif, A. Bergam, Z. Mghazli) A posteriori estimators for the finite volume discretization of an elliptic problem.
    Numer. Alg. 34, 127-136 (2003)
20. A posteriori error estimation techniques for non-linear elliptic and parabolic pdes.
    Revue Européenne pour les Eléments Finis 9, 377-401 (2000)
21. (with A. Papastavrou) Adaptive finite element methods for convection-diffusion problems. A computational comparison.
    Numer. Meth. Appl. Mech. Engrg. 189, 449-462 (2000)
22. (with C. Bernardi) Adaptive finite element methods for elliptic equations with non-smooth coefficients.
    Numer. Math. 85, 579 - 608 (2000)
23. (with G. Kunert) Edge residuals dominate a posteriori error estimates for linear finite element methods on anisotropic triangular and tetrahedral meshes.
    Numer. Math. 86, 283 - 303 (2000)
24. Error estimates for some quasi-interpolation operators.
    RAIRO M2AN 33, 695 - 713 (1999)
25. A note on polynomial approximation in Sobolev spaces.
    RAIRO M2AN 33, 715 - 719 (1999)
26. (with C. Carstensen) Edge residuals dominate a posteriori error estimates for low order finite element methods.
    SIAM J. Numer. Anal. 36, 1571 - 1587 (1999)
27. A review of a posteriori error estimation techniques for elasticity problems.
    Comput. Meth. Appl. Mech. Engrg. 176, 419-440 (1999)
28. Robust a posteriori error estimators for singularly perturbed reaction-diffusion equations.
    Numer. Math. 78, 479 - 493 (1998)
29. A posteriori error estimates for non-linear problems. L^r(0,T;W^1,r)-error estimates for finite element discretizations of parabolic equations.
    Numer. Meth. for PDE  14, 487 - 518 (1998)
30. A posteriori error estimates for non-linear problems. L^r(0,T;L^r)-error estimates for finite element discretizations of parabolic equations.
    Math. Comput. 67 (224), 1335 - 1360 (1998)
31. A posteriori error estimators for convection-diffusion equations.
    Numer. Math. 80, 641 - 663 (1998)
32. A posteriori error estimates for non-linear problems. L^r-error estimates for finite element discretizations of elliptic equations.
    RAIRO M2AN 32, 817 - 842 (1998)
33. (with L. Tobiska) Analysis of a streamline diffusion finite element method for the Stokes and Navier-Stokes equations.
    SIAM J. Numer. Anal. 33, 107 - 127 (1996)
34. (with D. Braess) A posteriori error estimators for the Raviart-Thomas element.
    SIAM J. Numer. Anal. 33, 2431 - 2444 (1996)
35. The stability of finite element methods.
    Numer. Meth. for PDE 11, 93 - 105 (1995)
36. A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques.
    J. Comput. Appl. Math. 50, 67 - 83 (1994)
37. A Posteriori Error Estimates for Non-Linear Problems. Finite Element Discretizations of Elliptic Equations.
    Math. Comput. 62 (206), 445 - 475 (1994)
38. A posteriori error estimators for the Stokes equations II. Non-conforming discretizations.
    Numer. Math. 60, 235 - 249 (1991)
39. Finite element approximation of incompressible Navier-Stokes equations with slip boundary condition II.
    Numer. Math. 59, 615 - 636 (1991)
40. (with D. Braess) Multi-grid methods for non-conforming finite element methods.
    SIAM J. Numer. Anal. 27, 979 - 986 (1990)
41. A posteriori error estimators for the Stokes equations.
    Numer. Math. 55, 309 - 325 (1989)
42. Multi-level algorithms for mixed problems II. Treatment of the mini-element.
    SIAM J. Numer. Anal. 25, 285 - 293 (1988)
43. Finite element approximation of incompressible Navier-Stokes equations with slip boundary condition.
    Numer. Math. 50, 697 - 721 (1987)
44. Mixed finite element approximation of the vector potential.
    Numer. Math. 50, 685 - 695 (1987)
45. Finite element approximation of steady Navier-Stokes equations with mixed boundary conditions.
    RAIRO Anal. Numér. 19, 461 - 475 (1985)
46. The contraction number of a multi-grid method with mesh ratio 2 for solving Poisson's equation.
    Linear Algebra Appl. 60, 113 - 128 (1984)
47. Error estimates for a mixed finite element approximation of the Stokes equations.
    RAIRO Anal. Numér. 18, 175 - 182 (1984)
48. A combined conjugate gradient - multi-grid algorithm for the numerical solution of the Stokes problem.
    IMA J. Numer. Anal. 4, 441 - 455 (1984)
49. A multi-level algorithm for mixed problems.
    SIAM J. Numer. Anal. 21, 264 - 271 (1984)
50. On the number of local best approximations by exponential sums.
    J. Approximation Th. 34, 306-323 (1982)
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Conference Proceedings

1. (with C. Bernardi and B. Métivet) Analyse numérique d'indicateurs d'erreur.
   In: Maillage et Adaptation (P. L. Georges; ed), Hèrmes, Paris, 2002
2. (with A. Papastavrou) A computational comparison of a posteriori error estimators for convection-diffusion problems.
   In: Computational Mechanics. New Trends and Applications (E. Oñate, S. R. Idelsohn, E. N. Dvorkin; eds.), CIMNE, Barcelona, 1998
3. A review of a posteriori error estimation techniques for elasticity problems.
   In: On new Advances in Adaptive Computational Methods in Mechanics (P. Ladevèze, J. T. Oden; eds.), pp. 257-274, Elsevier 1998
4. Non-overlapping domain decomposition methods.
   In: Computational Science for the 21st Century (J. Periaux; ed.), Wiley, 1997
5. The equivalence of a posteriori error estimators.
   In: Proceedings of the 10th GAMM Seminar Kiel (W. Hackbusch; ed.), Vieweg, Braunschweig, 1995
6. A Posteriori Error Estimates for Non-Linear Problems.
   In: Numerical Methods for the Navier-Stokes Equations (F.-K. Hebeker, R. Rannacher, G. Wittum; eds.), pp. 288-297, Notes on Numerical Fluid Mechanics Vol. 47, Vieweg, Braunschweig, 1994
7. A posteriori error estimators and adaptive mesh-refinement techniques for the Navier-Stokes equations.
   In: Incompressible CFD - Trends and Advances (M. D. Gunzburger, R. A. Nicolaides; eds.), pp. 447-477, Cambridge University Press, 1993
8. A posteriori error estimators and adaptive mesh-refinement for a mixed finite element discretization of the Navier-Stokes equations.
   In: Numerical Treatment of the Navier-Stokes Equations, Proc. of the 5th GAMM-Seminar, Kiel, Jan. 1989 (W. Hackbusch, R. Rannacher; eds.), pp. 145-152, Vieweg, Braunschweig, 1990
9. Mixed finite element approximation of a fluid flow problem.
   In: Mathematics of Finite Elements and Applications V (J. R. Whiteman; ed.), pp. 335-342, Academic Press, London, 1985
10. Numerical solution of mixed finite element problems.
    In: Efficient Solution of Elliptic Systems (W. Hackbusch; ed.), pp. 132-144, Vieweg, Braunschweig, 1984
11. A preconditioned conjugate residual algorithm for the Stokes problem.
    In: Advances in Multi-Grid Methods (D. Braess, W. Hackbusch, U. Trottenberg; eds.), pp. 112-118, Vieweg, Braunschweig, 1984
12. The contraction number of a multi-grid method.
    ZAMM 63, T386-T387 (1983)
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arXiv

1. (with F. Tantardini) Robust a posteriori error estimators with error dominated oscillation for the reaction-diffusion equation.
   arXiv
2. (with F. Tantardini) Quasi-monotonicity and robust localization with continuous piecewise polynomials.
   arXiv
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Reports

1. (with F. Tantardini and A. Veeser) H^-1approximation with piecewise polynomials.
   Report, Universität Bochum, October 2016
2. (with F. Tantardini and A. Veeser) Tree approximation in the H^-1-norm with piecewise polynomials.
   Report, Universität Bochum, October 2016
3. A posteriori error estimates for non-linear parabolic equations.
   Universität Bochum, December 2004
   (download)
4. A posteriori error estimates for linear parabolic equations.
   Universität Bochum, October 2004
   (download)
5. Non-overlapping domain decomposition methods interpreted as multiplicative subspace correction algorithms.
   Universität Bochum, October 2004
   (download)
6. On the constants in some inverse inequalities for finite element functions.
   Universität Bochum, May 1999
   (download)
7. A posteriori error estimates for non-linear problems. Finite element discretizations of parabolic equations.
   Universität Bochum, March 1995
8. Fehlerschätzer für Finite-Element-Diskretisierungen in der linearen Elastizitätstheorie.
   Universität Bochum, April 1994
9. On the stability of Petrov-Galerkin formulations of the Stokes equations.
   Universität Zürich, June 1990
10. On the preconditioning of non-conforming solenoidal finite element approximations of the Stokes equation.
    Univeristät Zürich, August 1989
11. Iterative methods for the numerical solution of mixed finite element approximations of the Stokes problem.
    Report Nr. 379, INRIA, 1985
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Lecture Notes

1. Einführung in die Numerische Mathematik.
   Universität Bochum, February 2018 (137 pages)
   (download)
2. Numerik I (Gewöhnliche Differentialgleichungen und Differenzenverfahren für partielle Differentialgleichungen).
   Universität Bochum, August 2018 (145 pages)
   (download)
3. Numerik II (Finite Elemente).
   Universität Bochum, June 2019 (147 pages)
   (download)
4. Finite Element Methoden für Navier-Stokes Gleichungen.
   Universität Bochum, September 2019 (176 pages)
   (download)
5. Optimierung.
   Universität Bochum, February 2020 (173 pages)
   (download)
6. Approximationstheorie.
   Universität Bochum, September 2020 (137 pages)
   (download)
7. Adaptive Finite Element Methods.
   Universität Bochum, February 2018 (129 pages)
   (download)
8. Computational Fluid Dynamics.
   Universität Bochum, February 2018 (121 pages)
   (download)
9. Numerical Methods and Stochastics. Part I: Numerics
   Universität Bochum, March 2011 (107 pages)
   (download)
10. Optimierung für Elektro- und Informationstechniker.
    Universität Bochum, March 2017 (100 pages)
    (download)
11. Vertiefung Numerische Mathematik für den Masterstudiengang UTRM.
    Universität Bochum, April 2010 (117 pages)
    (download)
12. Numerische Mathematik für Maschinenbauer und Umwelttechniker.
    Universität Bochum, September 2006 (108 pages)
    (download)
13. Mathematik für Maschinenbauer, Bauingenieure und Umwelttechniker.
    Universität Bochum, February 2008 (543 pages)
    (download)
14. Analysis.
    Universität Bochum, August 2006 (479 pages)
    (download)
15. A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques.
    Universität Zürich, May 1993 (Notes of a course given at the TU Magdeburg; 102 pages)
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Handouts

1. Computational Fluid Dynamics.
   Lecture Series, Bochum, Summer term 2019
   (download)
2. Adaptive Finite Element Methods.
   Lecture Series, Bochum, winter term 2018/19
   (download)
3. Adaptive finite element methods for non-stationary convection-diffusion problems.
   Lecture, Tübingen, July 2017
   (download)
4. Robust a posteriori error estimates for stabilized finite element discretizations of non-stationary convection-diffusion problems.
   Lecture, Oberwolfach, January 2017
   (download)
5. Robust a posteriori error estimates for stabilized FEM.
   Lecture, Milan, February 2014
   (download)
6. A posteriori error estimates for the biharmonic equation.
   Lecture, Milan, February 2013
   (download)
7. Robust a posteriori error estimates for non-stationary convection-diffusion problems.
   Lecture, Magdeburg, June 2013
   (download)
8. Beyond luck. Mathematics and games.
   Lecture, Milan, November 2012
   (download)
9. A posteriori error analysis of space-time finite element discretizations of the time-dependent Stokes equations.
   Lecture, Milan, February 2011
   (download)
10. Numerical Methods and Stochastics. Part I: Numerical Methods.
    Lecture Series, Bochum, Summer term 2011
    (download)
11. Computational Fluid Dynamics.
    PhD course, Milan, March 2010
    (download)
12. Vertiefung Numerische Mathematik für den Masterstudiengang UTRM.
    Lecture Series, Bochum, Summer term 2010
    (download)
13. Methematische Knobeleien. Eine Einführung in die mathematische Dankweise.
    Lecture, Bochum, Girls Day April 2010
    (download)
14. Constant-free a posteriori error estimates.
    Lecture, Duisburg, May 2010
    (download)
15. Mathematik und Spiel. Ohne Glück zum Sieg.
    Lecture, Bochum, October 2009
    (download)
16. A posteriori error analysis of the method of characteristics.
    Lecture, Kirchzarten, September 2009
    (download)
17. Explicit upper bounds for dual norms of residuals.
    Lecture, Paris, October 2008
    (download)
18. A review of robust a posteriori error estimates.
    Lecture, Milan, September 2007
    (download)
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