Professor John W Barrett
- Department of Mathematics, Imperial College London, London SW7 2AZ, UK
- Room No : 6M44
- Telephone No. : +44 (0)20 7594 8529 (office)
- Email:
j.barrett@ic.ac.uk
Research Interests :
- General Research Interests : Numerical Analysis,
Partial Differential Equations
- Particular Research Interests : Finite Element Approximation of
Nonlinear
Partial Differential Equations, Error Bounds,
Degenerate Equations, Phase Separation, Cahn-Hilliard Systems,
Phase Field Approximations, Void Electromigration/Stressmigration,
Thin Film Flows, Surfactants, Superconductivity, Critical State Problems,
Polymers, Liquid Crystals, Harmonic Maps,
Geometric Evolution Equations, Monge-Kantorovich Problem
Some Recent Papers :
- (with Patrick A. Wood)
Finite element approximation of
a model vortex problem
,
Numer. Funct. Anal. Optimiz.
16 (1995), 261--285.
- (with Patrick A. Wood)
The finite element approximation of
a coupled reaction-diffusion problem
with non-Lipschitz nonlinearities
, Numer. Math.
71 (1995), 135--157.
- (with James F. Blowey)
An error bound for the finite element
approximation
of the Cahn-Hilliard equation
with logarithmic free energy
, Numer. Math.
72 (1995), 1--20.
- (with Wenbin Liu)
Quasi-norm error bounds for the finite element
approximation of some degenerate
parabolic equations and variational inequalities
, Numer. Funct. Anal. Optimiz.
16 (1995), 1309--1321.
- (with Wenbin Liu)
Finite element approximation of some degenerate
monotone quasilinear elliptic systems
, SIAM J. Numer. Anal.
33 (1996), 88--106.
- (with James F. Blowey)
An error bound for the finite element
approximation of a model for phase separation
of a multi-component alloy
, IMA J. Numer. Anal.
16 (1996), 257--287.
- (with Peter Knabner)
Finite element approximation of transport of reactive
solutes in porous media,
Part 1: Error estimates for non-equilibrium adsorption processes
, SIAM J. Numer. Anal.
34 (1997), 201--227.
- (with Peter Knabner)
Finite element approximation of transport of reactive
solutes in porous media,
Part 2: Error estimates for equilibrium adsorption processes
, SIAM J. Numer. Anal.
34 (1997), 455--479.
- (with James F. Blowey)
Finite element approximation of a model for phase separation
of a multi-component alloy with non-smooth free energy
, Numer. Math.
77 (1997), 1--34.
- (with James F. Blowey)
Finite element approximation of a model for phase separation
of a multi-component alloy with
a concentration dependent mobility matrix
, IMA J. Numer. Anal.
18 (1998), 287--328.
- (with James F. Blowey and Harald Garcke)
Finite element approximation of a fourth order nonlinear
degenerate parabolic equation
, Numer. Math.
80 (1998), 525--556.
- (with Peter Knabner)
An improved error bound for a Lagrange Galerkin method
for contaminant transport with non-Lipschitzian adsorption
kinetics
, SIAM J. Numer. Anal.
35 (1998), 1862--1882.
- (with Weizhu Bao)
A priori and a posteriori error bounds for a nonconforming
finite element approximation of a non-Newtonian flow
, RAIRO M2AN.
32 (1998), 843--858.
- (with James F. Blowey)
Finite element approximation of the Cahn-Hilliard equation
with concentration dependent mobility
, Math. Comp.
68 (1999), 487--517.
- (with James F. Blowey)
An improved error bound for a
finite element approximation of a model for phase separation
of a multi-component alloy
, IMA J. Numer. Anal.
19 (1999), 147--168.
- (with James F. Blowey)
Finite element approximation of a model for phase separation
of a multi-component alloy with non-smooth free energy and
a concentration dependent mobility matrix
, M3AS.
9 (1999), 627--663.
- (with Mathias Schneider)
Finite element approximation of a semilinear elliptic
problem with a singular nonlinearity
, Numer. Math.
82 (1999), 21--56.
- (with James F. Blowey)
An optimal error bound for a
finite element approximation of a model for phase separation
of a multi-component alloy with non-smooth free energy
, RAIRO M2AN.
33 (1999), 971--987.
- (with James F. Blowey and Harald Garcke)
Finite element approximation of the Cahn-Hilliard equation with
degenerate mobility
, SIAM J. Numer. Anal.
37 (1999), 286--318.
- (with Leonid Prigozhin)
Bean's critical-state model as the p
--> infinity limit of an evolutionary p-Laplacian equation
, J. Nonlinear Anal.
42 (2000), 977--993.
- (with James F. Blowey)
An improved error bound for a
finite element approximation of a model for phase separation
of a multi-component alloy with a concentration dependent
mobility matrix
, Numer. Math.
88 (2001), 255--297.
- (with James F. Blowey and Harald Garcke)
On fully practical finite element approximations of
degenerate Cahn-Hilliard equation systems
, RAIRO M2AN.
35 (2001), 713--748.
- (with James F. Blowey)
Finite element approximation of a degenerate Allen-Cahn\Cahn-Hilliard
system
, SIAM J. Numer. Anal.
39 (2001), 1598--1624.
- (with James F. Blowey)
Finite element approximation of an Allen-Cahn\Cahn-Hilliard
system
, IMA J. Numer. Anal.
22 (2002), 11--71.
- (with Robert Nürnberg)
Finite element approximation of a nonlinear degenerate
parabolic system describing bacterial pattern formation
, Interfaces and Free Boundaries
4 (2002), 277--307.
- (with Harald Garcke and Robert Nürnberg)
Finite element approximation of surfactant spreading on a thin film
, SIAM J. Numer. Anal.
41 (2003), 1427--1464.
-
(with Stephen Langdon and Robert Nürnberg)
Finite element approximation of a sixth order degenerate parabolic
equation, Numer. Math.
96
(2004), 401--434.
- (with Robert 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.
- (with Robert Nürnberg
and Vanessa Styles)
Finite element approximation
of a phase field model for void electromigration
, SIAM J. Numer. Anal.
42 (2004), 738--772.
- (with James Blowey)
Finite element approximation
of a nonlinear cross-diffusion population model
, Numer. Math.
98
(2004), 195--221.
- (with Robert Nürnberg)
Finite element approximation
of a Stefan problem with degenerate Joule heating
, RAIRO M2AN.
38
(2004), 633--652.
- (with Christoph Schwab and Endre Süli)
Existence of global weak solutions for some polymeric flow models
, M3AS.
15
(2005), 939--983.
- (with Harald Garcke and Robert Nürnberg)
Finite element approximation of a phase field model for surface diffusion of voids in a
stressed interconnect
, Math. Comp.
75
(2006), 7--41.
.
- (with Xiaobing Feng and Andreas Prohl)
Convergence of a fully discrete finite element method
for a degenerate parabolic system modelling nematic liquid crystals
with
variable degree of orientation
, M2AN.
40
(2006), 175--200.
- (with Robert Nürnberg and Mark Warner)
Finite element
approximation of soluble surfactant spreading on a thin film
,
SIAM J. Numer. Anal.
40
(2006), 1218--1247.
- (with Leonid Prigozhin)
Dual formulations in critical state problems
,
Interfaces and Free Boundaries
8 (2006), 347--368.
- (with Harald Garcke and Robert Nürnberg)
A parametric finite element method for fourth order geometric evolution
equations
,
J. Comp. Phys. 222 (2007), 441--467.
- (with Soeren Bartels, Xiaobing Feng and Andreas Prohl)
A convergent and constraint-preserving finite element method for
the p-harmonic flow into spheres
,
SIAM J. Numer. Anal.
45 (2007), 905--927.
- (with Harald Garcke and Robert Nürnberg)
A phase field model for the electromigration
of intergranular voids
,
Interfaces and Free Boundaries
9 (2007), 171--210.
- (with Harald Garcke and Robert Nürnberg)
On the variational approximation of combined
second and fourth order geometric evolution
equations
,
SIAM J. Sci. Comp.
29 (2007), 1006--1041.
- (with Klaus Deckelnick)
Existence, uniqueness and approximation of a doubly-degenerate
nonlinear parabolic system modelling bacterial evolution
,
M3AS.
17 (2007), 1095--1128.
- (with Endre Süli)
Existence of global weak solutions
to some regularized kinetic models for dilute polymers
, SIAM Multiscale Modeling and Simulation
6
(2007), 506--546.
- (with Leonid Prigozhin)
A mixed formulation of the Monge-Kantorovich equations
,
M2AN. 41
(2007), 1041--1060.
- (with Harald Garcke and Robert Nürnberg)
On sharp interface limits of Allen-Cahn/Cahn-Hilliard
variational inequalities
,
Discrete Cont. Dyn. S.
1
(2008), 1--14.
- (with Harald Garcke and Robert Nürnberg)
A varaiational formulation of anisotropic geometric evolution equations
in higher dimensions
,
Numer. Math. 109
(2008), 1--44.
- (with Harald Garcke and Robert Nürnberg)
On the parametric finite element approximation of evolving hypersurfaces in R^3
,
J. Comp. Phys. 227
(2008), 4281--4307.
- (with Harald Garcke and Robert Nürnberg)
Numerical approximation of anisotropic geometric evolution equations
in the plane
,
IMA J. Numer. Anal.
28 (2008), 292--300.
- (with Endre Süli)
Existence of global weak solutions to dumbbell models for dilute polymers
with microscopic cut-off
, M3AS.
18 (2008), 935--971.
- (with Linda El Alaoui)
Finite element approximation of a two-layered liquid film in the presence of insoluble surfactants
, M2AN.
42
(2008), 749--776.
- (with Harald Garcke and Robert Nürnberg)
Parametric approximation of Willmore flow and related geometric evolution equations
,
SIAM J. Sci. Comp.
31
(2008), 225--253.
- (with Xiaobing Feng and Andreas Prohl)
On p-harmonic map heat flows for 1 =< p < infinity
and their finite element approximations
, SIAM J. Math. Anal.
40
(2008), 1471--1498.
- (with Endre Süli)
Existence of global weak solutions to coupled Navier--Stokes--Fokker--Planck
systems: A brief survey
, Novi Sad J. Math.
38
(2008), 7--14.
- (with Leonid Prigozhin)
Partial L1 Monge-Kantorovich problem: Variational formultion and numerical approximation
,
Interfaces and Free Boundaries
11
(2009), 201--238.
- (with Endre Süli)
Numerical approximation of corotational dumbbell models for dilute polymers
, IMA J. Numer. Anal.
29
(2009), 937--959.
- (with Harald Garcke and Robert Nürnberg)
Numerical approximation of gradient flows for closed curves in R^d
,
IMA J. Numer. Anal.
30
(2010), 4--60.
- (with Harald Garcke and Robert Nürnberg)
Parametric approximation of surface clusters driven by isotropic and anisotropic
surface energies
,
Interfaces and Free Boundaries
12
(2010), 187--234.
- (with Endre Süli)
Existence of global weak solutions to Fokker--Planck
and Navier--Stokes--Fokker--Planck
equations in kinetic models of dilute polymers
,
Discrete Cont. Dyn. S.
3
(2010), 371--408.
- (with Leonid Prigozhin)
A quasi-variational inequality problem in superconductivity
,
M3AS.
20
(2010), 679--706.
- (with Harald Garcke and Robert Nürnberg)
On stable parametric finite element methods for Stefan problem
and Mullins--Sekerka problem with applications to dendritic growth
,
J. Comp. Phys.
229
(2010), 6270--6299.
- (with Harald Garcke and Robert 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.
- (with Harald Garcke and Robert Nürnberg)
The approximation of planar curve evolutions by stable fully implicit finite
element schemes that equidistribute
,
Numer. Meth. Part. D. E.
27
(2011), 1--30.
- (with Endre Süli)
Finite element approximation of kinetic dilute polymer models
with microscopic cut-off
,
M2AN.
45
(2011), 39--89.
- (with Endre Süli)
Existence and equilibration of global weak solutions to
kinetic models for dilute polymers I:
Finitely extensible bead-spring
chains
,
M3AS.
21
(2011), 1211--1289.
- (with Sebastien Boyaval)
Existence and approximation of a (regularized) Oldroyd-B model
,
M3AS.
21
(2011), 1783--1837.
- (with Harald Garcke and Robert Nürnberg)
Parametric approximation of isotropic and anisotropic elastic flow for closed and open curves
,
Numer. Math.
120
(2012), 489--542.
- (with Endre Süli)
Reflections on Dubinskii's nonlinear compact embedding theorem
,
Publications de l'Institut Mathematique
(to appear).
- (with Endre Süli)
Existence and equilibration of global weak solutions to
kinetic models for dilute polymers II:
Hookean-type models
,
M3AS.
(to appear).
- (with Endre Süli)
Finite element approximation of finitely extensible nonlinear elastic dumbbell models
for dilute polymers
,
M2AN.
(to appear).
- (with Harald Garcke and Robert Nürnberg)
Elastic flow with junctions: variational approximation and applications to nonlinear splines
,
M3AS.
(to appear).
If you have problems accessing some of these papers, you could try the very
innovative
Spir@l digital repository.
A nearly complete list of my publications can be found
here.
JWB February 2012