Imperial College London, Department of Mathematics
Robert Nürnberg
Senior Lecturer -
Teaching
Exchange Programme Coordinator for the Department of Mathematics -
Information
Room No: |
6m14 |
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Telephone No: |
+44 (0)20 759 48572 (office) |
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E-mail: |
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
Publications
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J.W. Barrett, H. Garcke and R. Nürnberg:
Variational discretization of axisymmetric curvature flows
, Numer. Math. (2019), to appear.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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J.W. Barrett, H. Garcke and R. Nürnberg:
Finite element approximation for the dynamics of asymmetric fluidic
biomembranes,
Math. Comp. 86 (2017), 1037--1069.
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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.
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M. Agnese and R. Nürnberg:
Fitted finite element discretization of two--phase Stokes flow,
Internat. J. Numer. Methods Fluids 82 (2016), 709--729.
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J.W. Barrett, H. Garcke and R. Nürnberg:
A stable numerical method for the dynamics of fluidic membranes,
Numer. Math. 134 (2016), 783--822.
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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.
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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.
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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]
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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.
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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.
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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.
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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.
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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.
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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.
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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]
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J.W. Barrett, H. Garcke and R. Nürnberg:
Stable phase field approximations of anisotropic solidification,
IMA J. Numer. Anal. 34 (2014), 1289--1327.
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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.
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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.
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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.
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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.
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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]
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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]
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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Ľ. Baňas and R. Nürnberg:
A multigrid method for the Cahn--Hilliard equation with obstacle potential,
Appl. Math. Comput. 213 (2009), 290--303.
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R. Nürnberg:
Numerical simulations of immiscible fluid clusters,
Appl. Numer. Math. 59 (2009), 1612--1628.
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Ľ. Baňas and R. Nürnberg:
Phase field computations for surface diffusion and void electromigration in
R^3, Comput. Vis. Sci. 12 (2009), 319--327.
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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.
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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.
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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.
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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.
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Ľ. Baňas and R. Nürnberg:
Adaptive finite element methods for Cahn--Hilliard equations,
J. Comp. Appl. Math. 218 (2008), 2--11.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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
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Numerical approximation of axisymmetric formulations for geometric
evolution equations,
Advanced Developments for Surface and Interface Dynamics -- Analysis and
Computation, Banff (Canada), 2018.
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Variational approximation of axisymmetric formulations for geometric
evolution equations,
Geometry, Analysis and Approximation of Variational Problems,
Freiburg (Germany), 2018.
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Numerical approximation of (anisotropic) surface diffusion,
RTG 2339: Interfaces, Complex Structures, and Singular Limits,
Regensburg (Germany), 2018.
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Numerical approximation of (crystalline) anisotropic surface diffusion,
Mathematical Aspects of Surface and Interface Dynamics 14,
Tokyo (Japan), 2017.
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Numerical Approximation of Phase Field Models,
Lecture series,
Summer School 2017 "Phase Field Models",
Graduate School TU Munich, Munich (Germany), 2017.
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Coupling bulk and surface PDEs: Numerical approximation of dynamic
biomembranes,
Workshop "Foundations of Numerical PDEs",
Foundations of Computational Mathematics 2017, Barcelona (Spain), 2017.
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Coupling Navier--Stokes to Willmore: Numerical approximation of dynamic
biomembranes,
Theme Session "Surface PDEs and related topics",
Free Boundary Problems 2017, Shanghai (China), 2017.
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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.
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Coupling Navier--Stokes to Willmore: Numerical approximation of dynamic
biomembranes,
Partial Differential Equations in Biology, Warwick (UK), 2017.
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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.
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Coupling Navier--Stokes to Willmore: Numerical approximation of dynamic
biomembranes,
Workshop "Geometric Partial Differential Equations: Surface and Bulk
Processes",
Oberwolfach (Germany), 2015.
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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.
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Stable finite element approximations of incompressible two-phase flow,
Recent Developments and Challenges in Interface and Free
Boundary Problems,
Warwick (UK), 2014.
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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.
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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.
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A semismooth Newton method for a gradient constrained minimization problem,
Focus Session "Optimization and Free Boundaries",
Free Boundary Problems 2012,
Regensburg (Germany), 2012.
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Parametric approximation of elastic flow for curves and curve networks,
Higher Order Problems in Geometric Analysis, Bath (UK), 2012.
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Numerical approximation of facetted pattern formation in snow crystal
growth, Minisymposium "Numerical Analysis", BAMC 2012,
London (UK), 2012.
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Parametric approximation of surface clusters driven by isotropic and
anisotropic surface energies,
Isoperimetric problems,
space-filling, and soap bubble geometry, ICMS Edinburgh (UK), 2012.
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Parametric approximation of elastic flow for curves and curve networks,
Workshop "Geometric Partial Differential Equations: Theory, Numerics and
Applications",
Oberwolfach (Germany), 2011.
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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.
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Numerical approximation of multicomponent surface diffusion,
Minisymposium "Advanced finite element techniques for nonlinear evolution
problems", ENUMATH 2011,
Leicester (UK), 2011.
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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.
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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
Robert Nürnberg
Last changed on 07/01/2019