Please check my new personal webpage at the University of Trento.

Robert Nürnberg

Senior Lecturer    -     Teaching

Exchange Programme Coordinator for the Department of Mathematics    -     Information

Research interests

• Numerical Analysis, (Nonlinear) Partial Differential Equations, Finite Element Approximations
• Geometric Evolution Equations, Free Boundary Problems, Scientific Computing
• More details on my research page.

Recent and upcoming organised events

• Invited organiser: Theme session Numerical Methods for Geometric PDEs, FBP 2020, Humboldt University, Berlin, 31 August -- 4 September 2020.
• Invited organiser: Theme session Numerics for Free Boundary Problems and related topics, FBP 2017, Jiao Tong University, Shanghai, 9--15 July 2017.
• Organiser: Workshop Biological Membranes: Modelling, Analysis and Numerics, Imperial College London, 7--8 January 2016.

Preprints

• M. Ebenbeck, H. Garcke and R. Nürnberg: Cahn--Hilliard--Brinkman systems for tumour growth, arXiv:2003.08314.
• J.W. Barrett, H. Garcke and R. Nürnberg: Stable approximations for axisymmetric Willmore flow for closed and open surfaces, arXiv:1911.01132.
• D. Antonopoulou, L. Banas, R. Nürnberg and A. Prohl: Numerical approximation of the stochastic Cahn--Hilliard equation near the sharp interface limit, arXiv:1905.11050.

Publications

1. J.W. Barrett, K. Deckelnick and R. Nürnberg: A finite element error analysis for axisymmetric mean curvature flow, IMA J. Numer. Anal. (2020), to appear.
2. H. Garcke and R. Nürnberg: Structure-preserving discretizations of gradient flows for axisymmetric two-phase biomembranes, IMA J. Numer. Anal. (2020), to appear.
3. 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.
4. 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]
5. J.W. Barrett, H. Garcke and R. Nürnberg: Numerical approximation of curve evolutions in Riemannian manifolds, IMA J. Numer. Anal. 40 (2020), 1601--1651.
6. J.W. Barrett, H. Garcke and R. Nürnberg: Stable discretizations of elastic flow in Riemannian manifolds, SIAM J. Numer. Anal. 57 (2019), 1987--2018.
7. W. Dörfler and R. Nürnberg: Discrete gradient flows for general curvature energies, SIAM J. Sci. Comput. 41 (2019), 2012--2036.
8. J.W. Barrett, H. Garcke and R. Nürnberg: Variational discretization of axisymmetric curvature flows, Numer. Math. 141 (2019), 791--837.
9. 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.
10. 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.
11. 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.
12. J.W. Barrett, H. Garcke and R. Nürnberg: Finite element approximation for the dynamics of fluidic two-phase biomembranes, M2AN Math. Model. Numer. Anal. 51 (2017), 2319--2366.
13. 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.
14. 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.
15. 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.
16. J.W. Barrett, H. Garcke and R. Nürnberg: Finite element approximation for the dynamics of asymmetric fluidic biomembranes, Math. Comp. 86 (2017), 1037--1069.
17. Ľ. Baňas and R. Nürnberg: Numerical approximation of a non-smooth phase-field model for multicomponent incompressible flow, M2AN Math. Model. Numer. Anal. 51 (2017), 1089--1117.
18. M. Agnese and R. Nürnberg: Fitted finite element discretization of two--phase Stokes flow, Internat. J. Numer. Methods Fluids 82 (2016), 709--729.
19. J.W. Barrett, H. Garcke and R. Nürnberg: A stable numerical method for the dynamics of fluidic membranes, Numer. Math. 134 (2016), 783--822.
20. 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.
21. 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.
22. 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]
23. 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.
24. 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.
25. 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.
26. J.W. Barrett, H. Garcke and R. Nürnberg: On the stable numerical approximation of two-phase flow with insoluble surfactant, M2AN Math. Model. Numer. Anal. 49 (2015), 421--458.
27. 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.
28. 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.
29. 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]
30. J.W. Barrett, H. Garcke and R. Nürnberg: Stable phase field approximations of anisotropic solidification, IMA J. Numer. Anal. 34 (2014), 1289--1327.
31. 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.
32. 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.
33. 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.
34. 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.
35. 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]
36. 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]
37. 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.
38. 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.
39. 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.
40. 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.
41. 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.
42. 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.
43. 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.
44. Ľ. Baňas and R. Nürnberg: A posteriori estimates for the Cahn--Hilliard equation with obstacle free energy, M2AN Math. Model. Numer. Anal. 43 (2009), 1003--1026.
45. Ľ. Baňas and R. Nürnberg: A multigrid method for the Cahn--Hilliard equation with obstacle potential, Appl. Math. Comput. 213 (2009), 290--303.
46. R. Nürnberg: Numerical simulations of immiscible fluid clusters, Appl. Numer. Math. 59 (2009), 1612--1628.
47. Ľ. Baňas and R. Nürnberg: Phase field computations for surface diffusion and void electromigration in R^3, Comput. Vis. Sci. 12 (2009), 319--327.
48. 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.
49. 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.
50. 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.
51. 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.
52. Ľ. Baňas and R. Nürnberg: Adaptive finite element methods for Cahn--Hilliard equations, J. Comp. Appl. Math. 218 (2008), 2--11.
53. 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.
54. 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.
55. 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.
56. 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.
57. 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.
58. 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.
59. 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.
60. 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.
61. J.W. Barrett and R. Nürnberg: Finite element approximation of a Stefan problem with degenerate Joule heating, M2AN Math. Model. Numer. Anal. 38 (2004), 633--652.
62. 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.
63. 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.
64. 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.
65. 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.
66. 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.
67. 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.
68. 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

• Numerical approximation of axisymmetric formulations for geometric evolution equations, Advanced Developments for Surface and Interface Dynamics -- Analysis and Computation, Banff (Canada), 2018.
• Variational approximation of axisymmetric formulations for geometric evolution equations, Geometry, Analysis and Approximation of Variational Problems, Freiburg (Germany), 2018.
• Numerical approximation of (anisotropic) surface diffusion, RTG 2339: Interfaces, Complex Structures, and Singular Limits, Regensburg (Germany), 2018.
• Numerical approximation of (crystalline) anisotropic surface diffusion, Mathematical Aspects of Surface and Interface Dynamics 14, Tokyo (Japan), 2017.
• Numerical Approximation of Phase Field Models, Lecture series, Summer School 2017 "Phase Field Models", Graduate School TU Munich, Munich (Germany), 2017.
• Coupling bulk and surface PDEs: Numerical approximation of dynamic biomembranes, Workshop "Foundations of Numerical PDEs", Foundations of Computational Mathematics 2017, Barcelona (Spain), 2017.
• Coupling Navier--Stokes to Willmore: Numerical approximation of dynamic biomembranes, Theme Session "Surface PDEs and related topics", Free Boundary Problems 2017, Shanghai (China), 2017.
• Stable finite element approximations of incompressible two-phase flow, Theme Session "Numerics for Free Boundary Problems and related topics", Free Boundary Problems 2017, Shanghai (China), 2017.
• Coupling Navier--Stokes to Willmore: Numerical approximation of dynamic biomembranes, Partial Differential Equations in Biology, Warwick (UK), 2017.
• Parametric finite element methods for the dynamics of fluidic membranes and vesicles, Minisymposium "Finite element methods for PDEs in time-dependent domain", MAFELAP 2016, Brunel University (UK), 2016.
• Coupling Navier--Stokes to Willmore: Numerical approximation of dynamic biomembranes, Workshop "Geometric Partial Differential Equations: Surface and Bulk Processes", Oberwolfach (Germany), 2015.
• Parametric finite element methods for two-phase flow and dynamic biomembranes Postgraduate ASI in Mathematical and Physical Sciences: Modelling, Numerical Analysis and Applications, Isaac Newton Institute, Cambridge (UK), 2015.
• Stable finite element approximations of incompressible two-phase flow, Recent Developments and Challenges in Interface and Free Boundary Problems, Warwick (UK), 2014.
• Stable approximation of Stefan problems with fully anisotropic Gibbs-Thomson law, Focus Session "Numerical methods for evolving hypersurfaces", Free Boundary Problems 2012, Regensburg (Germany), 2012.
• Numerical approximation of facetted pattern formation in snow crystal growth, Focus Session "Crystalline interface evolution and related singular curvature flow", Free Boundary Problems 2012, Regensburg (Germany), 2012.
• A semismooth Newton method for a gradient constrained minimization problem, Focus Session "Optimization and Free Boundaries", Free Boundary Problems 2012, Regensburg (Germany), 2012.
• Parametric approximation of elastic flow for curves and curve networks, Higher Order Problems in Geometric Analysis, Bath (UK), 2012.
• Numerical approximation of facetted pattern formation in snow crystal growth, Minisymposium "Numerical Analysis", BAMC 2012, London (UK), 2012.
• Parametric approximation of surface clusters driven by isotropic and anisotropic surface energies, Isoperimetric problems, space-filling, and soap bubble geometry, ICMS Edinburgh (UK), 2012.
• Parametric approximation of elastic flow for curves and curve networks, Workshop "Geometric Partial Differential Equations: Theory, Numerics and Applications", Oberwolfach (Germany), 2011.
• Numerical analysis of variational inequalities with pointwise gradient constraints, Minisymposium "Variational inequalities and MPECs in function space: Analysis, numerics, and applications", IFIP 2011, Berlin (Germany), 2011.
• Numerical approximation of multicomponent surface diffusion, Minisymposium "Advanced finite element techniques for nonlinear evolution problems", ENUMATH 2011, Leicester (UK), 2011.
• Parametric approximation of geometric evolution equations and applications to the modelling of snowflake growth, Workshop "New Directions in Simulation, Control and Analysis for Interfaces and Free Boundaries", Oberwolfach (Germany), 2010.
• Parametric finite element approximations for Willmore flow and Helfrich flow, One Day Workshop on Biological Membranes, Regensburg (Germany), 2009.
• Adaptive finite elements for the simulation of immiscible fluid clusters, Adaptive Finite Elements: Analysis and Application, Kirchzarten (Germany), 2009.
• Numerical approximation of gradient flows for curve networks and surface clusters, New Directions in Computational PDEs, University of Warwick (UK), 2009.
• Numerical approximation of gradient flows for curves and surfaces, Numerical Solution of Complex PDE Systems, 5th MIDNAG Meeting, Leicester (UK), 2008.
• Variational approximation of geometric evolution equations, Minisymposium "PDE models of interface evolution and applications", Equadiff 07, Vienna (Austria), 2007.
• Parametric finite element approximation of evolving hypersurfaces in R^3, Minisymposium "Computational advances in evolving interfaces", ICIAM 07, Zurich (Switzerland), 2007.
• Variational approximation of anisotropic geometric evolution equations, Nonlocal and abstract parabolic equations and their applications, Bedlewo (Poland), 2007.
• Variational approximation of combined second and fourth order geometric evolution equations, Minisymposium "Morphometric Multiscale Surface Science", BAMC 2007, Bristol (UK), 2007.
• Variational approximation of anisotropic geometric evolution equations, Workshop "Anisotropic Motion Laws", Oberwolfach (Germany), 2006.
• Introduction to ALBERTA, CNAMMM "Multiscale" Research Network Meeting, Sussex (UK), 2005. [pdf]
• Finite element approximation of a phase field model for multicomponent surface diffusion, Free Boundary Problems 2005, Coimbra (Portugal), 2005.
• Finite element approximation of a void electromigration model, Workshop "Interphase 2003", Isaac Newton Institute, Cambridge (UK), 2003. [link]
• Finite element approximation of a nonlinear degenerate parabolic system describing bacterial pattern formation, X-th Summer School in Numerical Analysis, Durham (UK), 2002.
• A two-stage planning model for power scheduling in a hydro-thermal system under uncertainty, 9th International Conference on Stochastic Programming, Berlin (Germany), 2001.

Recent PhD Students

• Marco Agnese (2013--2017)
• Andrea Sacconi (2011--2015)
• Edward J. W. Tucker (2008--2012, joint supervision with John W. Barrett)

Miscellaneous

• I translated the book Linear Functional Analysis: An Application-Oriented Introduction by Hans Wilhelm Alt.
• A method for finding the distance from a point to an ellipse, and the distance from a point to an ellipsoid.
• A method for calculating the volume and centroid of a polyhedron in 3d. Note that the polyhdron need not be convex.