### 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
- Third year tutor: ma.yrentry14@imperial.ac.uk

- 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, Crystal Growth, Two-Phase Flow, Monge-Kantorovich Problem, Biomembranes

- (with Patrick A. Wood)
Finite element approximation of
a model vortex problem,
*Numer. Funct. Anal. Optimiz.***16**(1995), 261--285. [doi] - (with Patrick A. Wood)
The finite element approximation of
a coupled reaction-diffusion problem
with non-Lipschitz nonlinearities,
*Numer. Math.***71**(1995), 135--157. [doi] - (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. [doi] - (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. [doi] - (with Wenbin Liu)
Finite element approximation of some degenerate
monotone quasilinear elliptic systems,
*SIAM J. Numer. Anal.***33**(1996), 88--106. [doi] - (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. [doi] - (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. [link] - (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. [link] - (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. [doi] - (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. [doi] - (with James F. Blowey and Harald Garcke)
Finite element approximation of a fourth order nonlinear
degenerate parabolic equation,
*Numer. Math.***80**(1998), 525--556. [doi] - (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. [link] - (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. [link] - (with James F. Blowey)
Finite element approximation of the Cahn-Hilliard equation
with concentration dependent mobility,
*Math. Comp.***68**(1999), 487--517. [doi] - (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. [doi] - (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. [doi] - (with Mathias Schneider)
Finite element approximation of a semilinear elliptic
problem with a singular nonlinearity,
*Numer. Math.***82**(1999), 21--56. [doi] - (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. [doi] - (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. [doi] - (with Leonid Prigozhin)
Bean's critical-state model as the p
--> infinity limit of an evolutionary p-Laplacian equation,
*Nonlinear Anal.***42**(2000), 977--993. [doi] - (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. [doi] - (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. [doi] - (with James F. Blowey)
Finite element approximation of a degenerate Allen-Cahn\Cahn-Hilliard
system,
*SIAM J. Numer. Anal.***39**(2001), 1598--1624. [doi] - (with James F. Blowey)
Finite element approximation of an Allen-Cahn\Cahn-Hilliard
system,
*IMA J. Numer. Anal.***22**(2002), 11--71. [doi] - (with Robert Nürnberg)
Finite element approximation of a nonlinear degenerate
parabolic system describing bacterial pattern formation,
*Interfaces and Free Boundaries***4**(2002), 277--307. [doi] - (with Harald Garcke and Robert Nürnberg)
Finite element approximation of surfactant spreading on a thin film,
*SIAM J. Numer. Anal.***41**(2003), 1427--1464. [doi] -
(with Stephen Langdon and Robert Nürnberg)
Finite element approximation of a sixth order degenerate parabolic
equation,
*Numer. Math.***96**(2004), 401--434. [doi] - (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. [doi] - (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. [doi] - (with James Blowey)
Finite element approximation
of a nonlinear cross-diffusion population model,
*Numer. Math.***98**(2004), 195--221. [doi] - (with Robert Nürnberg)
Finite element approximation
of a Stefan problem with degenerate Joule heating,
*RAIRO M2AN.***38**(2004), 633--652. [doi] - (with Christoph Schwab and Endre Süli)
Existence of global weak solutions for some polymeric flow models,
*M3AS.***15**(2005), 939--983. [doi] - (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. [doi] - (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. [doi] - (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. [doi] - (with Leonid Prigozhin)
Dual formulations in critical state problems,
*Interfaces and Free Boundaries***8**(2006), 347--368. [doi] - (with Harald Garcke and Robert Nürnberg)
A parametric finite element method for fourth order geometric evolution
equations,
*J. Comp. Phys.***222**(2007), 441--467. [doi] - (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. [doi] - (with Harald Garcke and Robert Nürnberg)
A phase field model for the electromigration
of intergranular voids,
*Interfaces and Free Boundaries***9**(2007), 171--210. [doi] - (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. [doi] - (with Klaus Deckelnick)
Existence, uniqueness and approximation of a doubly-degenerate
nonlinear parabolic system modelling bacterial evolution,
*M3AS.***17**(2007), 1095--1128. [doi] - (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. [doi] - (with Leonid Prigozhin)
A mixed formulation of the Monge-Kantorovich equations,
*M2AN.***41**(2007), 1041--1060. [doi] - (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. [doi] - (with Harald Garcke and Robert Nürnberg)
A varaiational formulation of anisotropic geometric evolution equations
in higher dimensions,
*Numer. Math.***109**(2008), 1--44. [doi] - (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. [doi] - (with Harald Garcke and Robert Nürnberg)
Numerical approximation of anisotropic geometric evolution equations
in the plane,
*IMA J. Numer. Anal.***28**(2008), 292--330. [doi] - (with Endre Süli)
Existence of global weak solutions to dumbbell models for dilute polymers
with microscopic cut-off,
*M3AS.***18**(2008), 935--971. [doi] - (with Linda El Alaoui)
Finite element approximation of a two-layered liquid film in the presence of insoluble surfactants,
*M2AN.***42**(2008), 749--776. [doi] - (with Harald Garcke and Robert Nürnberg)
Parametric approximation of Willmore flow and related geometric evolution equations,
*SIAM J. Sci. Comp.***31**(2008), 225--253. [doi] - (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. [doi] - (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. [ link] - (with Leonid Prigozhin)
Partial L1 Monge-Kantorovich problem: Variational formulation and numerical approximation,
*Interfaces and Free Boundaries***11**(2009), 201--238. [doi] - (with Endre Süli)
Numerical approximation of corotational dumbbell models for dilute polymers,
*IMA J. Numer. Anal.***29**(2009), 937--959. [doi] - (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. [doi] - (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. [doi] - (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. [doi] - (with Leonid Prigozhin)
A quasi-variational inequality problem in superconductivity,
*M3AS.***20**(2010), 679--706. [doi] - (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. [doi] - (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. [doi] - (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. [doi] - (with Endre Süli)
Finite element approximation of kinetic dilute polymer models
with microscopic cut-off,
*M2AN.***45**(2011), 39--89. [doi] - (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. [doi] - (with Sebastien Boyaval)
Existence and approximation of a (regularized) Oldroyd-B model,
*M3AS.***21**(2011), 1783--1837. [doi] - (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. [doi] - (with Endre Süli)
Finite element approximation of finitely extensible nonlinear elastic dumbbell models
for dilute polymers,
*M2AN.***46**(2012), 949--978. [doi] - (with Endre Süli)
Existence and equilibration of global weak solutions to
kinetic models for dilute polymers II:
Hookean-type models,
*M3AS.***22**(2012), 1150024 (84 pages). [doi] - (with Endre Süli)
Reflections on Dubinskii's nonlinear compact embedding theorem,
*Publications de l'Institut Mathematique***91**(2012), 95--110. [doi] - (with Harald Garcke and Robert Nürnberg)
Numerical computations of faceted pattern formation in snow crystal growth,
*Phys. Rev. E***86**(2012), 011604 (14 pages). [doi] - (with Harald Garcke and Robert Nürnberg)
Elastic flow with junctions: variational approximation and applications to nonlinear splines,
*M3AS.***22**(2012), 1250037 (57 pages). [doi] - (with Leonid Prigozhin)
Electric field formulation for thin film magnetization problems,
*Supercond. Sci. Technol.***25**(2012), 104022 (8 pages). [doi] - (with Endre Süli)
Existence of global weak solutions to finitely extensible nonlinear
bead-spring chain models for dilute polymers
with variable density and viscosity,
*J. Differential Equations***253**(2012), 3610--3677. [doi] - (with Klaus Deckelnick)
Existence and approximation of a nonlinear degenerate parabolic system
modelling acid-mediated tumour invasion,
*Interfaces and Free Boundaries***14**(2012), 343--363. [doi] - (with Harald Garcke and Robert Nürnberg)
Finite element approximation of one-sided Stefan problems
with anisotropic, approximately crystalline, Gibbs-Thomson law,
*Adv. Differential Equations***18**(2013), 383--432. [link] - (with Leonid Prigozhin)
A quasi-variational inequality problem arising in the modeling of growing sandpiles,
*M2AN.***47**(2013), 1133--1165. [doi] - (with Leonid Prigozhin and Vladimir Sokolovsky)
Transport current and magnetization problems for thin type-II superconducting films,
*Supercond. Sci. Technol.***26**(2013), 105009 (9 pages). [doi] - (with Harald Garcke and Robert Nürnberg)
On the stable discretization of strongly
anisotropic phase field models with applications to crystal growth,
*ZAMM.***93**(2013), 719--732. [doi] - (with Harald Garcke and Robert Nürnberg)
Eliminating spurious velocities with a stable approximation of viscous incompressible two-phase Stokes flow,
*Comp. Meth. Appl. Mech. Engng.***267**(2013), 511--530. [doi] [arXiv] - (with Harald Garcke and Robert Nürnberg)
Phase field models versus parametric front tracking methods: Are they accurate and computationally efficient?,
*Commun. Comput. Phys.***15**(2014), 506--555. [doi] [arXiv] - (with Leonid Prigozhin)
Existence and approximation of a mixed formulation for thin film magnetization
problems in superconductivity,
*M3AS.***24**(2014), 991--1015. [doi] [link] - (with Leonid Prigozhin)
Lakes and rivers in the landscape: a quasi-variational approach,
*Interfaces and Free Boundaries***16**(2014), 269--296. [doi] [link] - (with Harald Garcke and Robert Nürnberg)
Stable phase field approximations of anisotropic solidification,
*IMA J. Numer. Anal.***34**(2014), 1289--1327. [doi] [arXiv] - (with Vladimir Sokolovsky and Leonid Prigozhin)
3D modeling of magnetic atom traps on type-II superconductor chips,
*Supercond. Sci. Technol.***27**(2014), 124004 (10 pages). [doi] [link] - (with Leonid Prigozhin)
Sandpiles and superconductors: Nonconforming linear finite element approximations for mixed
formulations of quasi-variational inequalities,
*IMA J. Numer. Anal.***35**(2015), 1--38. [doi] [arXiv] - (with Harald Garcke and Robert Nürnberg)
A stable parametric finite element discretization of
two-phase Navier--Stokes flow,
*J. Sci. Comp.***63**(2015), 78--117. [doi] [arXiv] - (with Harald Garcke and Robert Nürnberg)
On the stable numerical approximation of
two-phase flow with insoluble surfactant,
*M2AN.***49**(2015), 421--458. [doi] [arXiv] - (with Harald Garcke and Robert Nürnberg)
Stable finite element approximations of
two-phase flow with soluble surfactant,
*J. Comp. Phys.***297**(2015), 530--564. [doi] - (with Harald Garcke and Robert Nürnberg)
Stable numerical approximation of
two-phase flow with a Boussinesq--Scriven fluid,
*Comm. Math. Sci.***13**(2015), 1829--1874. [doi] [arXiv] - (with Harald Garcke and Robert Nürnberg)
Numerical computations of the dynamics of fluidic membranes and vesicles,
*Phys. Rev. E***92**(2015), 052704 (14 pages). [doi] [arXiv] - (with Endre Süli)
Existence of global weak solutions to compressible
isentropic finitely extensible bead-spring chain models for dilute polymers,
*M3AS.***26**(2016), 469--568. [doi] [arXiv] - (with Endre Süli)
Existence of global weak solutions to compressible
isentropic finitely extensible bead-spring chain models for dilute polymers:
the two-dimensional case,
*J. Differential Equations***261**(2016), 592--626. [doi] - (with Harald Garcke and Robert Nürnberg)
Computational parametric Willmore flow with spontaneous curvature
and area difference elasticity effects,
*SIAM J. Numer. Anal.***54**(2016), 1732--1762. [doi] - (with Harald Garcke and Robert Nürnberg)
A stable numerical method for the dynamics of fluidic membranes,
*Numer. Math.***134**(2016), 783--822. [doi] - (with Leonid Prigozhin, Vladimir Sokolovsky and Sergey E. Zirka)
On the energy-based variational model for vector magnetic hysteresis,
*IEEE Trans. Magnetics***52**(2016), 7301211 (11 pages). [doi] - (with Harald Garcke and Robert Nürnberg)
Finite element approximation for the dynamics of asymmetric fluidic biomembranes,
*Math. Comp.***86**(2017), 1037--1069. [doi] - (with Harald Garcke and Robert Nürnberg)
Stable variational approximations of boundary value problems for Willmore flow with Gaussian curvature,
*IMA J. Numer. Anal.*(to appear). - (with Yong Lu and Endre Süli)
Existence of large-data finite-energy global weak solutions to a compressible
Oldroyd-B model,
*Comm. Math. Sci.*(to appear). - (with Klaus Deckelnick and Vanessa Styles)
Numerical analysis for a system coupling curve evolution to reaction-diffusion on the curve,
*SIAM J. Numer. Anal.*(to appear).

If you have problems accessing some of these papers, you could try the Spir@l digital repository.

A nearly complete list of my publications can be found here.

JWB February 2017