Imperial College London, Department of Mathematics
Robert Nürnberg
Senior Lecturer 
Teaching
Exchange Programme Coordinator for the Department of Mathematics 
Information
Room No: 
6m14 


Telephone No: 
+44 (0)20 759 48572 (office) 


Email: 
rn@ic.ac.uk 
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, 915 July 2017.
 Organiser:
Workshop Biological Membranes: Modelling, Analysis and
Numerics, Imperial College London, 78 January 2016.
Preprints

M. Ebenbeck, H. Garcke and R. Nürnberg:
CahnHilliardBrinkman systems for tumour growth, arXiv:2003.08314.

H. Garcke and R. Nürnberg:
Structure preserving discretisations of gradient flows for
axisymmetric twophase biomembranes, arXiv:2003.03127.

J.W. Barrett, K. Deckelnick and R. Nürnberg:
A finite element error analysis for axisymmetric mean curvature flow,
arXiv:1911.05398.

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 CahnHilliard
equation near the sharp interface limit, arXiv:1905.11050.
Publications

M. Agnese and R. Nürnberg:
Fitted front tracking methods for twophase incompressible NavierStokes
flow: Eulerian and ALE finite element discretizations,
Int. J. Numer. Anal. Model. (2019), to appear.

J.W. Barrett, H. Garcke and R. Nürnberg:
Parametric finite element approximations of curvature driven
interface evolutions,
Handb. Numer. Anal. 21 (2020), 275423.
[arXiv]

J.W. Barrett, H. Garcke and R. Nürnberg:
Stable discretizations of elastic flow in Riemannian manifolds,
SIAM J. Numer. Anal. 57 (2019), 19872018.

W. Dörfler and R. Nürnberg:
Discrete gradient flows for general curvature energies,
SIAM J. Sci. Comput. 41 (2019), 20122036.

J.W. Barrett, H. Garcke and R. Nürnberg:
Numerical approximation of curve evolutions in Riemannian manifolds,
IMA J. Numer. Anal. (2019), to appear.

J.W. Barrett, H. Garcke and R. Nürnberg:
Variational discretization of axisymmetric curvature flows,
Numer. Math. 141 (2019), 791837.

J.W. Barrett, H. Garcke and R. Nürnberg:
Finite element methods for fourth order axisymmetric geometric
evolution equations,
J. Comput. Phys. 376 (2019), 733766.

J.W. Barrett, H. Garcke and R. Nürnberg:
Gradient flow dynamics of twophase biomembranes: Sharp interface
variational formulation and finite element approximation,
SMAI J. Comput. Math. 4 (2018), 151195.

H. Garcke, K. F. Lam, R. Nürnberg and E. Sitka:
A multiphase CahnHilliardDarcy model for tumour growth with
necrosis, Math. Models Methods Appl. Sci. 28 (2018),
525577.

J.W. Barrett, H. Garcke and R. Nürnberg:
Finite element approximation for the dynamics of fluidic twophase
biomembranes, M2AN Math. Model. Numer. Anal. 51 (2017),
23192366.

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), 16571709.

S. Aland, A. Hahn, C. Kahle and R. Nürnberg:
Comparative simulations of Taylor flow with surfactants based on
sharp and diffuseinterface methods,
in: Transport Processes at Fluidic Interfaces
(D. Bothe and A. Reusken eds.), Birkhäuser (2017), 639679.

R. Nürnberg and E. Tucker:
Stable finite element approximation of a CahnHilliardStokes
system coupled to an electric field,
European J. Appl. Math. 28 (2017), 470498.

J.W. Barrett, H. Garcke and R. Nürnberg:
Finite element approximation for the dynamics of asymmetric fluidic
biomembranes,
Math. Comp. 86 (2017), 10371069.

Ľ. Baňas and R. Nürnberg:
Numerical approximation of a nonsmooth phasefield model for multicomponent
incompressible flow,
M2AN Math. Model. Numer. Anal. 51 (2017), 10891117.

M. Agnese and R. Nürnberg:
Fitted finite element discretization of twophase Stokes flow,
Internat. J. Numer. Methods Fluids 82 (2016), 709729.

J.W. Barrett, H. Garcke and R. Nürnberg:
A stable numerical method for the dynamics of fluidic membranes,
Numer. Math. 134 (2016), 783822.

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), 17321762.

R. Nürnberg and A. Sacconi:
A fitted finite element method for the numerical approximation of
void electrostress migration,
Appl. Numer. Math. 104 (2016), 204217.

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]

R. Nürnberg and E. Tucker:
Finite element approximation of a phase field model arising in nanostructure
patterning, Numer. Methods Partial Differential Equations 31
(2015), 18901924.

J.W. Barrett, H. Garcke and R. Nürnberg:
Stable numerical approximation of twophase flow with a BoussinesqScriven
surface fluid, Commun. Math. Sci. 13 (2015), 18291874.

J.W. Barrett, H. Garcke and R. Nürnberg:
Stable finite element approximations of twophase flow with soluble
surfactant, J. Comput. Phys. 297 (2015),
530564.

J.W. Barrett, H. Garcke and R. Nürnberg:
On the stable numerical approximation of twophase flow with insoluble
surfactant, M2AN Math. Model. Numer. Anal. 49 (2015),
421458.

J.W. Barrett, H. Garcke and R. Nürnberg:
A stable parametric finite element discretization of twophase
NavierStokes flow, J. Sci. Comput. 63 (2015),
78117.

R. Nürnberg and A. Sacconi:
An unfitted finite element method for the numerical approximation of
void electromigration,
J. Comput. Appl. Math. 270 (2014), 531544.

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), 506555.
[arXiv]

J.W. Barrett, H. Garcke and R. Nürnberg:
Stable phase field approximations of anisotropic solidification,
IMA J. Numer. Anal. 34 (2014), 12891327.

J.W. Barrett, H. Garcke and R. Nürnberg:
Eliminating spurious velocities with a stable approximation of viscous
incompressible twophase Stokes flow,
Comput. Methods Appl. Mech. Engrg. 267 (2013), 511530.

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), 719732.

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.

Ľ. Baňas, A. NovickCohen and R. Nürnberg:
The degenerate and nondegenerate deep quench obstacle problem: A
numerical comparison,
Netw. Heterog. Media 8 (2013), 3764.

J.W. Barrett, H. Garcke and R. Nürnberg:
Finiteelement approximation of onesided Stefan problems with
anisotropic, approximately crystalline, GibbsThomson law,
Adv. Differential Equations 18 (2013), 383432.
[arXiv]

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]

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.

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), 489542.

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),
130.

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), 519556.

J.W. Barrett, H. Garcke and R. Nürnberg:
On stable parametric finite element methods for the Stefan problem and the
MullinsSekerka problem with applications to dendritic growth,
J. Comput. Phys. 229 (2010), 62706299.

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), 187234.

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), 460.

Ľ. Baňas and R. Nürnberg:
A posteriori estimates for the CahnHilliard equation with obstacle free
energy,
M2AN Math. Model. Numer. Anal. 43 (2009), 10031026.

Ľ. Baňas and R. Nürnberg:
A multigrid method for the CahnHilliard equation with obstacle potential,
Appl. Math. Comput. 213 (2009), 290303.

R. Nürnberg:
Numerical simulations of immiscible fluid clusters,
Appl. Numer. Math. 59 (2009), 16121628.

Ľ. Baňas and R. Nürnberg:
Phase field computations for surface diffusion and void electromigration in
R^3, Comput. Vis. Sci. 12 (2009), 319327.

J.W. Barrett, H. Garcke and R. Nürnberg:
Parametric approximation of Willmore flow and related geometric
evolution equations,
SIAM J. Sci. Comput. 31 (2008), 225253.

Ľ. Baňas and R. Nürnberg:
Finite element approximation of a three dimensional phase field model
for void electromigration,
J. Sci. Comput. 37 (2008), 202232.

J.W. Barrett, H. Garcke and R. Nürnberg:
A variational formulation of anisotropic geometric evolution equations
in higher dimensions,
Numer. Math. 109 (2008), 144.

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), 42814307.

Ľ. Baňas and R. Nürnberg:
Adaptive finite element methods for CahnHilliard equations,
J. Comp. Appl. Math. 218 (2008), 211.

J.W. Barrett, H. Garcke and R. Nürnberg:
Numerical approximation of anisotropic geometric evolution equations
in the plane,
IMA J. Numer. Anal. 28 (2008), 292330.

J.W. Barrett, H. Garcke and R. Nürnberg:
On sharp interface limits of AllenCahn/CahnHilliard
variational inequalities,
Discrete Contin. Dyn. Syst. Ser. S. 1 (2008), 114.

H. Garcke, R. Nürnberg and V. Styles:
Stress and diffusioninduced interface motion: Modelling and numerical
simulations, European J. Appl. Math. 18 (2007),
631657.

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), 10061041.

J.W. Barrett, H. Garcke and R. Nürnberg:
A phase field model for the electromigration of intergranular voids,
Interfaces Free Bound. 9 (2007), 171210.

J.W. Barrett, H. Garcke and R. Nürnberg:
A parametric finite element method for fourth order geometric evolution
equations,
J. Comput. Phys. 222 (2007), 441467.

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), 12181247.

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), 741.

J.W. Barrett and R. Nürnberg:
Finite element approximation of a Stefan problem with degenerate Joule
heating,
M2AN Math. Model. Numer. Anal. 38 (2004), 633652.

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),
738772.

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), 323363.

J.W. Barrett, S. Langdon and R. Nürnberg:
Finite element approximation of a sixth order nonlinear degenerate
parabolic equation,
Numer. Math. 96 (2004), 401434.

J.W. Barrett, H. Garcke and R. Nürnberg:
Finite element approximation of surfactant spreading on a thin film,
SIAM J. Numer. Anal. 41 (2003), 14271464.

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), 623636.

J.W. Barrett and R. Nürnberg:
Finite element approximation of a nonlinear degenerate parabolic system
describing bacterial pattern formation,
Interfaces Free Bound. 4 (2002), 277307.

R. Nürnberg and W. Römisch:
A twostage planning model for power scheduling in a hydrothermal system under
uncertainty,
Optim. Eng. 3 (2002), 355378.
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 NavierStokes 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 twophase flow,
Theme Session "Numerics for Free Boundary Problems and related topics",
Free Boundary Problems 2017, Shanghai (China), 2017.

Coupling NavierStokes 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 timedependent domain",
MAFELAP 2016,
Brunel University (UK), 2016.

Coupling NavierStokes to Willmore: Numerical approximation of dynamic
biomembranes,
Workshop "Geometric Partial Differential Equations: Surface and Bulk
Processes",
Oberwolfach (Germany), 2015.

Parametric finite element methods for twophase 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 twophase flow,
Recent Developments and Challenges in Interface and Free
Boundary Problems,
Warwick (UK), 2014.

Stable approximation of Stefan problems with fully anisotropic
GibbsThomson 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,
spacefilling, 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,
Xth Summer School in Numerical Analysis, Durham (UK), 2002.
 A twostage planning model for power scheduling in a hydrothermal
system under uncertainty,
9th International Conference on Stochastic Programming,
Berlin (Germany), 2001.
Recent PhD Students
 Marco Agnese (20132017)
 Andrea Sacconi (20112015)
 Edward J. W. Tucker (20082012, joint supervision with John W. Barrett)
Miscellaneous
Robert Nürnberg
Last changed on 19/03/2020