University of Trento, Department of Mathematics

Robert Nürnberg

Associate professor



Room No: 269
Telephone No: +39 0461 281619 (office)
E-mail: robert.nurnberg (at) unitn.it


Research interests


Recent and upcoming organised events


Preprints

Publications

  1. H. Garcke and R. Nürnberg: A finite element method for anisotropic crystal growth on surfaces, Int. J. Numer. Anal. Model. (2024), (accepted for publication).
  2. H. Garcke, K. F. Lam, R. Nürnberg and A. Signori: Complex pattern formation governed by a Cahn--Hilliard--Swift--Hohenberg system: Analysis and numerical simulations, Math. Models Methods Appl. Sci., 34 (2024), 2055--2097.
  3. T. Eto, H. Garcke and R. Nürnberg: A structure-preserving finite element method for the multi-phase Mullins--Sekerka problem with triple junctions, Numer. Math. 156 (2024), 1479--1509.
  4. K. Deckelnick and R. Nürnberg: Discrete anisotropic curve shortening flow in higher codimension, IMA J. Numer. Anal. (2024), (to appear).
  5. H. Garcke, R. Nürnberg and Q. Zhao: Arbitrary Lagrangian--Eulerian finite element approximations for axisymmetric two-phase flow, Comput. Math. Appl. 155 (2024), 209--223.
  6. K. Deckelnick and R. Nürnberg: A novel finite element approximation of anisotropic curve shortening flow, Interfaces Free Bound. 25 (2023), 671--708.
  7. H. Garcke, R. Nürnberg and Q. Zhao: Unfitted finite element methods for axisymmetric two-phase flow, J. Sci. Comput. 97 (2023), 14.
  8. K. Deckelnick and R. Nürnberg: Discrete hyperbolic curvature flow in the plane, SIAM J. Numer. Anal. 61 (2023), 1835--1857.
  9. R. Nürnberg: A structure preserving front tracking finite element method for the Mullins--Sekerka problem, J. Numer. Math. 31 (2023), 137--155.
  10. H. Garcke, R. Nürnberg and Q. Zhao: Structure-preserving discretizations of two-phase Navier--Stokes flow using fitted and unfitted approaches, J. Comput. Phys. 489 (2023), 112276.
  11. H. Garcke, K. F. Lam, R. Nürnberg and A. Signori: Phase field topology optimisation for 4D printing, ESAIM Control Optim. Calc. Var. 29 (2023), 24.
  12. H. Garcke, K. F. Lam, R. Nürnberg and A. Signori: Overhang penalization in additive manufacturing via phase field structural topology optimization with anisotropic energies, Appl. Math. Optim. 87 (2023), 44.
  13. L. Carini, M. Jensen and R. Nürnberg: Deep learning for gradient flows using the Brezis--Ekeland principle, Arch. Math. (Brno) 59 (2023), 249--261.
  14. K. Deckelnick and R. Nürnberg: An unconditionally stable finite element scheme for anisotropic curve shortening flow, Arch. Math. (Brno) 59 (2023), 263--274.
  15. H. Garcke, P. Knopf, R. Nürnberg and Q. Zhao: A diffuse-interface approach for solid-state dewetting with anisotropic surface energies, J. Nonlinear Sci. 33 (2023), 34.
  16. W. Bao, H. Garcke, R. Nürnberg and Q. Zhao: A structure-preserving finite element approximation of surface diffusion for curve networks and surface clusters, Numer. Methods Partial Differential Equations 39 (2023), 759--794.
  17. W. Bao, H. Garcke, R. Nürnberg and Q. Zhao: Volume-preserving parametric finite element methods for axisymmetric geometric evolution equations, J. Comput. Phys. 460 (2022), 111180.
  18. J. Eyles, R. Nürnberg and V. Styles: Finite element approximation of a phase field model for tumour growth, Port. Math. 78 (2021), 341--365.
  19. K. Deckelnick and R. Nürnberg: Error analysis for a finite difference scheme for axisymmetric mean curvature flow of genus-0 surfaces, SIAM J. Numer. Anal. 59 (2021), 2698--2721.
  20. H. Garcke and R. Nürnberg: Numerical approximation of boundary value problems for curvature flow and elastic flow in Riemannian manifolds, Numer. Math. 149 (2021), 375--415.
  21. M. Ebenbeck, H. Garcke and R. Nürnberg: Cahn--Hilliard--Brinkman systems for tumour growth, Discrete Contin. Dyn. Syst. Ser. S. 14 (2021), 3989--4033.
  22. D. Antonopoulou, Ľ. Baňas, R. Nürnberg and A. Prohl: Numerical approximation of the stochastic Cahn--Hilliard equation near the sharp interface limit, Numer. Math. 147 (2021), 505--551.
  23. H. Garcke and R. Nürnberg: Structure-preserving discretizations of gradient flows for axisymmetric two-phase biomembranes, IMA J. Numer. Anal. 41 (2021), 1899--1940.
  24. J.W. Barrett, K. Deckelnick and R. Nürnberg: A finite element error analysis for axisymmetric mean curvature flow, IMA J. Numer. Anal. 41 (2021), 1641--1667.
  25. J.W. Barrett, H. Garcke and R. Nürnberg: Stable approximations for axisymmetric Willmore flow for closed and open surfaces, ESAIM Math. Model. Numer. Anal. 55 (2021), 833--885.
  26. M. Agnese and R. Nürnberg: Fitted front tracking methods for two-phase incompressible Navier--Stokes flow: Eulerian and ALE finite element discretizations, Int. J. Numer. Anal. Model. 17 (2020), 613--642.
  27. J.W. Barrett, H. Garcke and R. Nürnberg: Parametric finite element approximations of curvature driven interface evolutions, Handb. Numer. Anal. 21 (2020), 275--423. [arXiv]
  28. J.W. Barrett, H. Garcke and R. Nürnberg: Numerical approximation of curve evolutions in Riemannian manifolds, IMA J. Numer. Anal. 40 (2020), 1601--1651.
  29. J.W. Barrett, H. Garcke and R. Nürnberg: Stable discretizations of elastic flow in Riemannian manifolds, SIAM J. Numer. Anal. 57 (2019), 1987--2018.
  30. W. Dörfler and R. Nürnberg: Discrete gradient flows for general curvature energies, SIAM J. Sci. Comput. 41 (2019), 2012--2036.
  31. J.W. Barrett, H. Garcke and R. Nürnberg: Variational discretization of axisymmetric curvature flows, Numer. Math. 141 (2019), 791--837.
  32. J.W. Barrett, H. Garcke and R. Nürnberg: Finite element methods for fourth order axisymmetric geometric evolution equations, J. Comput. Phys. 376 (2019), 733--766.
  33. J.W. Barrett, H. Garcke and R. Nürnberg: Gradient flow dynamics of two-phase biomembranes: Sharp interface variational formulation and finite element approximation, SMAI J. Comput. Math. 4 (2018), 151--195.
  34. H. Garcke, K. F. Lam, R. Nürnberg and E. Sitka: A multiphase Cahn--Hilliard--Darcy model for tumour growth with necrosis, Math. Models Methods Appl. Sci. 28 (2018), 525--577.
  35. J.W. Barrett, H. Garcke and R. Nürnberg: Finite element approximation for the dynamics of fluidic two-phase biomembranes, ESAIM Math. Model. Numer. Anal. 51 (2017), 2319--2366.
  36. J.W. Barrett, H. Garcke and R. Nürnberg: Stable variational approximations of boundary value problems for Willmore flow with Gaussian curvature, IMA J. Numer. Anal. 37 (2017), 1657--1709.
  37. S. Aland, A. Hahn, C. Kahle and R. Nürnberg: Comparative simulations of Taylor flow with surfactants based on sharp- and diffuse-interface methods, in: Transport Processes at Fluidic Interfaces (D. Bothe and A. Reusken eds.), Birkhäuser (2017), 639--679.
  38. R. Nürnberg and E. Tucker: Stable finite element approximation of a Cahn--Hilliard--Stokes system coupled to an electric field, European J. Appl. Math. 28 (2017), 470--498.
  39. J.W. Barrett, H. Garcke and R. Nürnberg: Finite element approximation for the dynamics of asymmetric fluidic biomembranes, Math. Comp. 86 (2017), 1037--1069.
  40. Ľ. Baňas and R. Nürnberg: Numerical approximation of a non-smooth phase-field model for multicomponent incompressible flow, ESAIM Math. Model. Numer. Anal. 51 (2017), 1089--1117.
  41. M. Agnese and R. Nürnberg: Fitted finite element discretization of two--phase Stokes flow, Internat. J. Numer. Methods Fluids 82 (2016), 709--729.
  42. J.W. Barrett, H. Garcke and R. Nürnberg: A stable numerical method for the dynamics of fluidic membranes, Numer. Math. 134 (2016), 783--822.
  43. J.W. Barrett, H. Garcke and R. Nürnberg: Computational parametric Willmore flow with spontaneous curvature and area difference elasticity effects, SIAM J. Numer. Anal. 54 (2016), 1732--1762.
  44. R. Nürnberg and A. Sacconi: A fitted finite element method for the numerical approximation of void electro-stress migration, Appl. Numer. Math. 104 (2016), 204--217.
  45. J.W. Barrett, H. Garcke and R. Nürnberg: Numerical computations of the dynamics of fluidic membranes and vesicles, Phys. Rev. E 92 (2015), 052704. [erratum]
  46. R. Nürnberg and E. Tucker: Finite element approximation of a phase field model arising in nanostructure patterning, Numer. Methods Partial Differential Equations 31 (2015), 1890--1924.
  47. J.W. Barrett, H. Garcke and R. Nürnberg: Stable numerical approximation of two-phase flow with a Boussinesq--Scriven surface fluid, Commun. Math. Sci. 13 (2015), 1829--1874.
  48. J.W. Barrett, H. Garcke and R. Nürnberg: Stable finite element approximations of two-phase flow with soluble surfactant, J. Comput. Phys. 297 (2015), 530--564.
  49. J.W. Barrett, H. Garcke and R. Nürnberg: On the stable numerical approximation of two-phase flow with insoluble surfactant, ESAIM Math. Model. Numer. Anal. 49 (2015), 421--458.
  50. J.W. Barrett, H. Garcke and R. Nürnberg: A stable parametric finite element discretization of two-phase Navier--Stokes flow, J. Sci. Comput. 63 (2015), 78--117.
  51. R. Nürnberg and A. Sacconi: An unfitted finite element method for the numerical approximation of void electromigration, J. Comput. Appl. Math. 270 (2014), 531--544.
  52. J.W. Barrett, H. Garcke and R. Nürnberg: Phase field models versus parametric front tracking methods: Are they accurate and computationally efficient?, Commun. Comput. Phys. 15 (2014), 506--555. [arXiv]
  53. J.W. Barrett, H. Garcke and R. Nürnberg: Stable phase field approximations of anisotropic solidification, IMA J. Numer. Anal. 34 (2014), 1289--1327.
  54. J.W. Barrett, H. Garcke and R. Nürnberg: Eliminating spurious velocities with a stable approximation of viscous incompressible two-phase Stokes flow, Comput. Methods Appl. Mech. Engrg. 267 (2013), 511--530.
  55. J.W. Barrett, H. Garcke and R. Nürnberg: On the stable discretization of strongly anisotropic phase field models with applications to crystal growth, ZAMM Z. Angew. Math. Mech. 93 (2013), 719--732.
  56. C. Rascon, A.O. Parry, R. Nürnberg, A. Pozzato, M. Tormen, L. Bruschi, G. Mistura: The order of condensation in capillary grooves, J. Phys.: Condens. Matter 25 (2013), 192101.
  57. Ľ. Baňas, A. Novick-Cohen and R. Nürnberg: The degenerate and non-degenerate deep quench obstacle problem: A numerical comparison, Netw. Heterog. Media 8 (2013), 37--64.
  58. J.W. Barrett, H. Garcke and R. Nürnberg: Finite-element approximation of one-sided Stefan problems with anisotropic, approximately crystalline, Gibbs--Thomson law, Adv. Differential Equations 18 (2013), 383--432. [arXiv]
  59. J.W. Barrett, H. Garcke and R. Nürnberg: Numerical computations of faceted pattern formation in snow crystal growth, Phys. Rev. E 86 (2012), 011604. [arXiv, Scientific American]
  60. J.W. Barrett, H. Garcke and R. Nürnberg: Elastic flow with junctions: Variational approximation and applications to nonlinear splines, Math. Models Methods Appl. Sci. 22 (2012), 1250037.
  61. J.W. Barrett, H. Garcke and R. Nürnberg: Parametric approximation of isotropic and anisotropic elastic flow for closed and open curves, Numer. Math. 120 (2012), 489--542.
  62. J.W. Barrett, H. Garcke and R. Nürnberg: The approximation of planar curve evolutions by stable fully implicit finite element schemes that equidistribute, Numer. Methods Partial Differential Equations 27 (2011), 1--30.
  63. J.W. Barrett, H. Garcke and R. Nürnberg: Finite element approximation of coupled surface and grain boundary motion with applications to thermal grooving and sintering, European J. Appl. Math. 21 (2010), 519--556.
  64. J.W. Barrett, H. Garcke and R. Nürnberg: On stable parametric finite element methods for the Stefan problem and the Mullins--Sekerka problem with applications to dendritic growth, J. Comput. Phys. 229 (2010), 6270--6299.
  65. J.W. Barrett, H. Garcke and R. Nürnberg: Parametric approximation of surface clusters driven by isotropic and anisotropic surface energies, Interfaces Free Bound. 12 (2010), 187--234.
  66. J.W. Barrett, H. Garcke and R. Nürnberg: Numerical approximation of gradient flows for closed curves in R^d, IMA J. Numer. Anal. 30 (2010), 4--60.
  67. Ľ. Baňas and R. Nürnberg: A posteriori estimates for the Cahn--Hilliard equation with obstacle free energy, ESAIM Math. Model. Numer. Anal. 43 (2009), 1003--1026.
  68. Ľ. Baňas and R. Nürnberg: A multigrid method for the Cahn--Hilliard equation with obstacle potential, Appl. Math. Comput. 213 (2009), 290--303.
  69. R. Nürnberg: Numerical simulations of immiscible fluid clusters, Appl. Numer. Math. 59 (2009), 1612--1628.
  70. Ľ. Baňas and R. Nürnberg: Phase field computations for surface diffusion and void electromigration in R^3, Comput. Vis. Sci. 12 (2009), 319--327.
  71. J.W. Barrett, H. Garcke and R. Nürnberg: Parametric approximation of Willmore flow and related geometric evolution equations, SIAM J. Sci. Comput. 31 (2008), 225--253.
  72. Ľ. Baňas and R. Nürnberg: Finite element approximation of a three dimensional phase field model for void electromigration, J. Sci. Comput. 37 (2008), 202--232.
  73. J.W. Barrett, H. Garcke and R. Nürnberg: A variational formulation of anisotropic geometric evolution equations in higher dimensions, Numer. Math. 109 (2008), 1--44.
  74. J.W. Barrett, H. Garcke and R. Nürnberg: On the parametric finite element approximation of evolving hypersurfaces in R^3, J. Comput. Phys. 227 (2008), 4281--4307.
  75. Ľ. Baňas and R. Nürnberg: Adaptive finite element methods for Cahn--Hilliard equations, J. Comp. Appl. Math. 218 (2008), 2--11.
  76. J.W. Barrett, H. Garcke and R. Nürnberg: Numerical approximation of anisotropic geometric evolution equations in the plane, IMA J. Numer. Anal. 28 (2008), 292--330.
  77. J.W. Barrett, H. Garcke and R. Nürnberg: On sharp interface limits of Allen--Cahn/Cahn--Hilliard variational inequalities, Discrete Contin. Dyn. Syst. Ser. S. 1 (2008), 1--14.
  78. H. Garcke, R. Nürnberg and V. Styles: Stress- and diffusion-induced interface motion: Modelling and numerical simulations, European J. Appl. Math. 18 (2007), 631--657.
  79. J.W. Barrett, H. Garcke and R. Nürnberg: On the variational approximation of combined second and fourth order geometric evolution equations, SIAM J. Sci. Comput. 29 (2007), 1006--1041.
  80. J.W. Barrett, H. Garcke and R. Nürnberg: A phase field model for the electromigration of intergranular voids, Interfaces Free Bound. 9 (2007), 171--210.
  81. J.W. Barrett, H. Garcke and R. Nürnberg: A parametric finite element method for fourth order geometric evolution equations, J. Comput. Phys. 222 (2007), 441--467.
  82. J.W. Barrett, R. Nürnberg and M.R.E. Warner: Finite element approximation of soluble surfactant spreading on a thin film, SIAM J. Numer. Anal. 44 (2006), 1218--1247.
  83. J.W. Barrett, H. Garcke and R. Nürnberg: Finite element approximation of a phase field model for surface diffusion of voids in a stressed solid, Math. Comp. 75 (2006), 7--41.
  84. J.W. Barrett and R. Nürnberg: Finite element approximation of a Stefan problem with degenerate Joule heating, ESAIM Math. Model. Numer. Anal. 38 (2004), 633--652.
  85. J.W. Barrett, R. Nürnberg and V. Styles: Finite element approximation of a phase field model for void electromigration, SIAM J. Numer. Anal. 42 (2004), 738--772.
  86. J.W. Barrett and R. Nürnberg: Convergence of a finite element approximation of surfactant spreading on a thin film in the presence of van der Waals forces, IMA J. Numer. Anal. 24 (2004), 323--363.
  87. J.W. Barrett, S. Langdon and R. Nürnberg: Finite element approximation of a sixth order nonlinear degenerate parabolic equation, Numer. Math. 96 (2004), 401--434.
  88. J.W. Barrett, H. Garcke and R. Nürnberg: Finite element approximation of surfactant spreading on a thin film, SIAM J. Numer. Anal. 41 (2003), 1427--1464.
  89. M.P. Nowak, R. Nürnberg, W. Römisch, R. Schultz and M. Westphalen: Stochastic programming for power production and trading under uncertainty, in: Mathematics -- Key Technology for the Future (W. Jäger and H.-J. Krebs eds.), Springer (2003), 623--636.
  90. J.W. Barrett and R. Nürnberg: Finite element approximation of a nonlinear degenerate parabolic system describing bacterial pattern formation, Interfaces Free Bound. 4 (2002), 277--307.
  91. R. Nürnberg and W. Römisch: A two-stage planning model for power scheduling in a hydro-thermal system under uncertainty, Optim. Eng. 3 (2002), 355--378.


Selected Talks



Former PhD Students



Miscellaneous


Robert Nürnberg
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Last changed on 24/10/2024