Robert Nürnberg

Associate professor

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.

Organised events

• Invited organiser: Minisymposium Finite element methods for geometric PDEs, Equadiff15, Masaryk University, Brno, 11--15 July 2022.
• Invited organiser: Minisymposium Numerical Methods for Geometric PDEs, FBP 2021, Humboldt University, Berlin, 13--17 September 2021.
• 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

• H. Garcke and R. Nürnberg: A parametric finite element method for the incompressible Navier--Stokes equations on an evolving surface, arXiv:2508.19198.
• R. Nürnberg and P. Pozzi: Minimal horizontal triods: Analysis and computation, arXiv:2507.15740.
• H. Garcke, R. Nürnberg and Q. Zhao: An energy-stable parametric finite element method for Willmore flow with normal-tangential velocity splitting, arXiv:2507.00193.
• T. Eto, H. Garcke and R. Nürnberg: A parametric finite element method for a degenerate multi-phase Stefan problem with triple junctions, arXiv:2505.13165.
• H. Garcke, R. Nürnberg and Q. Zhao: Stable fully practical finite element methods for axisymmetric Willmore flow, arXiv:2505.06195.
• H. Garcke, K. F. Lam, R. Nürnberg and A. Signori: On a Cahn--Hilliard equation for the growth and division of chemically active droplets modeling protocells, arXiv:2503.09581.
• K. Deckelnick and R. Nürnberg: Second order in time finite element schemes for curve shortening flow and curve diffusion, arXiv:2502.19277.

Publications

1. H. Garcke, R. Nürnberg and Q. Zhao: Stable fully discrete finite element methods with BGN tangential motion for Willmore flow of planar curves, J. Sci. Comput. 105 (2025), 45.
2. H. Garcke, R. Nürnberg, S. Praetorius and G. Zhang: Isoparametric finite element methods for mean curvature flow and surface diffusion, J. Comput. Phys. 539 (2025), 114248.
3. K. Deckelnick and R. Nürnberg: Finite element schemes with tangential motion for fourth order geometric curve evolutions in arbitrary codimension, Numer. Math. 157 (2025), 1313--1346.
4. H. Garcke, R. Nürnberg and Q. Zhao: A variational front-tracking method for multiphase flow with triple junctions, Math. Comp. (2025), to appear.
5. H. Garcke, R. Nürnberg and D. Trautwein: Parametric finite element approximation of two-phase Navier--Stokes flow with viscoelasticity, IMA J. Numer. Anal. (2025), to appear.
6. H. Garcke and R. Nürnberg: A finite element method for anisotropic crystal growth on surfaces, Int. J. Numer. Anal. Model. 22 (2025), 614--636.
7. K. Deckelnick and R. Nürnberg: On the numerical approximation of hyperbolic mean curvature flows for surfaces, Comput. Methods Appl. Mech. Engrg. 437 (2025), 117800.
8. K. Deckelnick and R. Nürnberg: Discrete anisotropic curve shortening flow in higher codimension, IMA J. Numer. Anal. 45 (2025), 36--67.
9. 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.
10. 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.
11. 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.
12. K. Deckelnick and R. Nürnberg: A novel finite element approximation of anisotropic curve shortening flow, Interfaces Free Bound. 25 (2023), 671--708.
13. H. Garcke, R. Nürnberg and Q. Zhao: Unfitted finite element methods for axisymmetric two-phase flow, J. Sci. Comput. 97 (2023), 14.
14. K. Deckelnick and R. Nürnberg: Discrete hyperbolic curvature flow in the plane, SIAM J. Numer. Anal. 61 (2023), 1835--1857.
15. R. Nürnberg: A structure preserving front tracking finite element method for the Mullins--Sekerka problem, J. Numer. Math. 31 (2023), 137--155.
16. 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.
17. 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.
18. 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.
19. L. Carini, M. Jensen and R. Nürnberg: Deep learning for gradient flows using the Brezis--Ekeland principle, Arch. Math. (Brno) 59 (2023), 249--261.
20. K. Deckelnick and R. Nürnberg: An unconditionally stable finite element scheme for anisotropic curve shortening flow, Arch. Math. (Brno) 59 (2023), 263--274.
21. 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.
22. 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.
23. 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.
24. J. Eyles, R. Nürnberg and V. Styles: Finite element approximation of a phase field model for tumour growth, Port. Math. 78 (2021), 341--365.
25. 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.
26. 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.
27. M. Ebenbeck, H. Garcke and R. Nürnberg: Cahn--Hilliard--Brinkman systems for tumour growth, Discrete Contin. Dyn. Syst. Ser. S. 14 (2021), 3989--4033.
28. 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.
29. H. Garcke and R. Nürnberg: Structure-preserving discretizations of gradient flows for axisymmetric two-phase biomembranes, IMA J. Numer. Anal. 41 (2021), 1899--1940.
30. 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.
31. 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.
32. 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.
33. 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]
34. J.W. Barrett, H. Garcke and R. Nürnberg: Numerical approximation of curve evolutions in Riemannian manifolds, IMA J. Numer. Anal. 40 (2020), 1601--1651.
35. J.W. Barrett, H. Garcke and R. Nürnberg: Stable discretizations of elastic flow in Riemannian manifolds, SIAM J. Numer. Anal. 57 (2019), 1987--2018.
36. W. Dörfler and R. Nürnberg: Discrete gradient flows for general curvature energies, SIAM J. Sci. Comput. 41 (2019), 2012--2036.
37. J.W. Barrett, H. Garcke and R. Nürnberg: Variational discretization of axisymmetric curvature flows, Numer. Math. 141 (2019), 791--837.
38. 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.
39. 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.
40. 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.
41. 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.
42. 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.
43. 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.
44. 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.
45. J.W. Barrett, H. Garcke and R. Nürnberg: Finite element approximation for the dynamics of asymmetric fluidic biomembranes, Math. Comp. 86 (2017), 1037--1069.
46. 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.
47. M. Agnese and R. Nürnberg: Fitted finite element discretization of two--phase Stokes flow, Internat. J. Numer. Methods Fluids 82 (2016), 709--729.
48. J.W. Barrett, H. Garcke and R. Nürnberg: A stable numerical method for the dynamics of fluidic membranes, Numer. Math. 134 (2016), 783--822.
49. 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.
50. 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.
51. 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]
52. 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.
53. 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.
54. 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.
55. 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.
56. 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.
57. 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.
58. 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]
59. J.W. Barrett, H. Garcke and R. Nürnberg: Stable phase field approximations of anisotropic solidification, IMA J. Numer. Anal. 34 (2014), 1289--1327.
60. 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.
61. 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.
62. 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.
63. 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.
64. 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]
65. 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]
66. 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.
67. 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.
68. 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.
69. 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.
70. 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.
71. 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.
72. 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.
73. 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.
74. Ľ. Baňas and R. Nürnberg: A multigrid method for the Cahn--Hilliard equation with obstacle potential, Appl. Math. Comput. 213 (2009), 290--303.
75. R. Nürnberg: Numerical simulations of immiscible fluid clusters, Appl. Numer. Math. 59 (2009), 1612--1628.
76. Ľ. Baňas and R. Nürnberg: Phase field computations for surface diffusion and void electromigration in R^3, Comput. Vis. Sci. 12 (2009), 319--327.
77. 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.
78. 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.
79. 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.
80. 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.
81. Ľ. Baňas and R. Nürnberg: Adaptive finite element methods for Cahn--Hilliard equations, J. Comp. Appl. Math. 218 (2008), 2--11.
82. 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.
83. 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.
84. 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.
85. 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.
86. 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.
87. 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.
88. 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.
89. 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.
90. 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.
91. 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.
92. 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.
93. 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.
94. 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.
95. 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.
96. 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.
97. 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

• Fluidic two-phase biomembranes: Numerical analysis and computations, Workshop "Finite Elements for Cell and Tissue Morphogenesis", Fréjus (France), 2024.
• Numerical analysis for fourth order geometric curve evolutions based on the DeTurck trick, Minisymposium "Surface evolution and harmonic maps", SciCADE 2024, Singapore (Singapore), 2024.
• Unfitted finite element methods for axisymmetric two-phase flow, Minisymposium "Recent Advances in Unfitted Finite Element Methods: Analysis, Algorithms, and Applications", Eccomas 2024, Lisbon (Portugal), 2024.
• Numerical approximation of solid-state dewetting with anisotropic surface energies, Workshop "Dynamics of interfaces: From applied math to physics and material science", Augsburg (Germany), 2024.
• Parametric finite element methods for Navier--Stokes equations on evolving surfaces, Workshop "Interfaces, Free Boundaries and Geometric Partial Differential Equations", Oberwolfach (Germany), 2024.
• Parametric finite element methods for Navier--Stokes equations on evolving surfaces, Workshop "Vector- and Tensor-Valued Surface PDEs", Dresden (Germany), 2023.
• Phase field simulations for solid-state dewetting with anisotropic surface energies, Minisymposium "Phase field approaches to modeling multiphase micro-flows", MNF 2023, Padua (Italy), 2023.
• Unfitted finite element methods for axisymmetric two-phase flow, Minisymposium "Structure-preserving unfitted finite element discretizations", ENUMATH 2023, Lisbon (Portugal), 2023.
• A generalized DeTurck trick for anisotropic curve shortening flow, Workshop "Phase Field Models and Free Boundary Problems", Regensburg (Germany), 2023.
• A structure-preserving finite element approximation of incompressible two-phase flow, Minisymposium "Computational methods for interface dynamics in fluids and solids", SciCADE 2022, Reykjavik (Iceland), 2022.
• A generalized DeTurck trick for anisotropic curve shortening flow, Minisymposium "Finite element methods for geometric PDEs", Equadiff15, Brno (Czech Republic), 2022.
• Fluidic two-phase biomembranes: Numerical analysis and computations, Minisymposium "Numerical methods for surface-bulk problems", Free Boundary Problems 2021, Berlin (Germany), 2021.
• 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: Numerical methods for free boundary problems", 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.

Former PhD Students

• Marco Agnese (Imperial College London, 2013--2017)
• Andrea Sacconi (Imperial College London, 2011--2015)
• Edward J. W. Tucker (Imperial College London, 2008--2012)

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.