2007

07-13: A. Madzvamuse, P.K. Maini
Velocity-induced numerical solutions of reaction-diffusion systems on continuously growing domains
submitted to J. Comp. Phys.

07-12: A. Cangiani and E. Suli.
The residual-free-bubble finite element method on anisotropic partitions
Accepted for publication in SIAM J. Numer. Anal. 2007

07-11: C. A. Haselwandter, D. D. Vvedensky
Renormalization of stochastic lattice models I: Basic formulation
submitted to Phys Rev E.

07-10: C. A. Haselwandter, D. D. Vvedensky
Multiscale theory of fluctuating interfaces: Renormalization of atomistic models
Phys Rev Lett, 98, 046102 (2007).

07-09: D. Blomker, M. Hairer, G. Pavliotis
Multiscale Analysis for SPDEs with Quadratic Nonlinearities
to appear in Nonlinearity, 05/2007

07-08: G. Pavliotis, A. M. Stuart, K.C. Zygalakis
Homogenization for Inertial Particles in a Random Flow.
Comm. Math. Sci., to appear, 2007

07-07: A. Madzvamuse, P.K. Maini
Pattern formation in growing domains

07-06: H. Garcke, R. Nuernberg, V. Styles,
Stress and diffusion induced interface motion: Modelling and numerical simulations
submitted to EJAM 2007

07-05: G. Dziuk, C. M. Elliott
An Eulerian level set method for partial differential equations equations on evolving surfaces
submitted for publication in Computing and Visualization in Science.

07-04: C. A. Haselwandter, D. D. Vvedensky
Fluctuation regimes of driven epitaxial surfaces
Europhys Lett. 77, 38004 (2007).

07-03: C. Schwab, E. Suli, R. A. Todor
Sparse finite element approximation of high-dimensional transport-dominated diffusion problems.
Submitted to M2AN, 2007.

07-02: D. Knezevic, E. Suli
Finite element methods for deterministic simultion of polymeric fluids.
submitted to Hungarian Journal of Applied Mathematics (Alkalmazott Matematikai Lapok), 2007.

07-01: P. Lin, P. Plechac
Numerical studies of a coarse-grained approximation of dynamics of an atomic chain.
accepted for publication in Intl. J. Multiscale Comp. Eng. (2007).

2006

06-31: E. Suli
A Gagliardo--Nirenberg inequality, with application to duality-based a posteriori error estimation in the $L_1$ norm.
Kragujevac Journal of Mathematics, Vol. 30, 2006.

06-30: P. Houston, E. Suli, T. P. Wihler
Discontinuous Galerkin finite element approximation of nonlinear second-order elliptic and hyperbolic systems.
Accepted for publication in IMA J. Numer. Anal., 2007.

06-29: C. Ortner, E. Suli,
Discontinuous Galerkin finite element approximation of nonlinear second-order elliptic and hyperbolic systems.
Accepted for publication in SIAM J. Numer. Anal., 2007

06-28: G. Dziuk, C.M. Elliott
Eulerian finite element method for parabolic equations on implicit surfaces.
submitted for publication in Interfaces Free Boundaries.

06-27: G. Dziuk, C.M. Elliott
Surface finite elements for parabolic equations
J. Comp. Math. 25 (2007)

06-26: D. Kay, V. Styles, R. Welford
Finite element approximation of a Cahn-Hilliard-Navier-Stokes system.
submitted to Interfaces and Free Boundaries, 2006.

06-25: D. Kay, R. Welford
Efficient numerical solution of Cahn-Hilliard-Navier-Stokes fluids in 2D
submitted SIAM J. Sci.Comp.

06-24: C. M. Elliott, S. A. McBeth
Numerical analysis of the TV regularization and $H^{-1}$ fidelity model for decomposing an image into cartoon plus texture
accepted for publication in IMA J. Numer. Anal.

06-23: G. Dziuk, C. M. Elliott
Finite elements on evolving surfaces.
IMA J. Num. Anal. 27 (2007), 262-292

06-22: J. W. Barrett, H. Garcke, R. Nuernberg
A variational formulation of anisotropic geometric evolution equations in higher dimensions.
submitted to Numer. Math.

06-21: M. A. Katsoulakis, P. Plechac, L. Rey-Bellet, D. K. Tsagkarogiannis
Mathematical strategies in the coarse-graining of extensive systems: error quantification and adaptivity.
accepted for publication in J. Non-Newtonian Fluid Mech. (2007)

06-20: A. M. Niehaus, D. Vlachos, J. S. Edwards, P. Plechac, R. Tribe
Microscopic simulation of epidermal growth on corralled membrane surfaces.
submitted to Biophysical Journal.

06-19: D. Knezevic
Finite element methods for deterministic simulation of polymeric fluids

06-18: J. W. Barrett, E. Suli
Existence of global weak solutions to kinetic models for dilute polymers
accepted for publication in SIAM Multiscale Modeling and Simulation.

06-17: C. Ortner, E. Suli
A-posteriori analysis and adaptive algorithms for the quasicontinuum method in one dimension

06-16: C. Ortner, E. Suli
A-priori analysis of the quasicontinuum method in one dimension

06-15: S. Berrone, E. Suli
Two-sided a posteriori error bounds for incompressible quasi-Newtonian flows

06-14: Christoph A. Haselwandter, Dimitri D. Vvedensky
Stochastic equation for the morphological evolution of heteroepitaxial thin films
Phys. Rev B 74 121408(R) (2006).

06-13: Christoph A. Haselwandter, Dimitri D. Vvedensky
Scaling of balistic deposition from a Langevin equation
Phys. Rev. E 73 040101 (R) (2006).

06-12: Markos A. Katsoulakis, Petr Plechac, Alexandros Sopasakis
Error control and analysis in coarse-graining of stochastic lattice dynamics
SIAM J. Numer. Anal., {44 (2006)}, 2270-2296.

06-11: Lubomir Banas, Robert Nurnberg
Finite Element Approximation of a Three Dimensional Phase Field Model for Void Electromigration
submitted to J. Sci. Comp.

06-10: John. W. Barrett, Harald Garcke, Robert Nurnberg
On sharp interface limits of Allen-Cahn/Cahn-Hilliard variational inequalities
accepted for publication in Discrete Cont. Dyn. Sys.

06-09: John. W. Barrett, Harald Garcke, Robert Nurnberg
On the Parametric Finite Element Approximation of Evolving Hypersurfaces in ${\mathbb R}^3$
submitted to J. Comp. Phys.

06-08: John. W. Barrett, Harald Garcke, Robert Nurnberg
Numerical Approximation of Anisotropic Geometric Evolution Equations
accepted for publication in IMA J. Numer. Anal.

06-07: John. W. Barrett, Harald Garcke, Robert Nurnberg
On the Variational Approximation of Combined Second and Fourth Order Geometric Evolution Equations
SIAM J. Sci. Comp. 29 (2007), 1006-1041.

06-06: John. W. Barrett, Harald Garcke, Robert Nurnberg
A Parametric Finite Element Method for Fourth Order Geometric Evolution Equations
J. Comp. Phys. 222 (2007), 441-467

06-05: G. Pavliotis, Andrew M Stuart
Parameter Estimation for Multiscale Diffusions
J. Stat. Phys. 127(4) 741-781, (2007).

06-04: Dwight. Barkley, Y. Kevrekidis, Andrew M Stuart
The Moment Map: Nonlinear Dynamics of Density Evolution Via a Few Moments
SIAM J. Appl. Dyn. Sys, 5(2006), 403-434.

06-03: Yvo Pokern, Andrew M Stuart, Petter Wiberg
Parameter estimation for partially observed hypoelliptic diffusions.

06-02: G. Pavliotis, Andrew M Stuart
Multiscale Methods.: Homogenization and Averaging.
Lecture Notes. Submitted to the publisher on 02/07

06-01: Markos A. Katsoulakis, Petr Plechac, Luc Rey-Bellet, Dimitrios K. Tsagkarogiannis
Coarse-graining schemes and a posteriori error estimates for stochastic lattice systems.
to appear in ESAIM Math. Modelling and Numer. Anal. (2007).

2005

05-18: O. Lakkis, Ch. Makridakis
Elliptic Reconstruction and A Posteriori Error Estimate for Fully Discrete Linear Parabolic Problems

05-17: M. Katsoulakis, G. T. Kossioris, O. Lakkis
A finite element method via noise regularization for the stochastic Allen-Cahn problem
Interfaces and Free Boundaries (2007), 9, 1-30

05-16: P. Houston, J. Giudice, E. Suli
Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: The scalar case.
IMA J. Numer. Anal. 25 (2005), 726-749.

05-15: J. W. Barrett, K. Deckelnick,
Existence, uniqueness and approximation of a doubly-degenerate nonlinear parabolic system modelling bacterial evolution.
accepted for publication in M3AS.

05-14: J. W. Barrett, S. Bartels, X. Feng, A. Prohl
A convergent and constraint-preserving finite element method for the p-harmonic flow into spheres.
SIAM J. Numer. Anal. 45 (2007), 905-927

05-13: P. Plechac
Mathematical tools for error analysis of coarse-graining of lattice systems.
Mathematisches Forschungsinstitut Oberwolfach 20/2005

05-12: E. Suli
Finite element approximation of high-dimensional transport-dominated diffusion problems
Published in: Luis-Miguel Pardo, Allan Pinkus, Endre Süli, Michael Todd (Eds.). Foundations of Computational Mathematics, Santander 2005. CUP, 2006.

05-11: C. Ortner
Continuum Limit of a One-Dimensional Atomistic Energy Based on Local Minimization
submitted to SIAM J. Math. Anal.

05-10: C. Ortner
Two Variational Techniques for the Approximation of Curves of Maximal Slope

05-09: G. Pavliotis, Andrew M Stuart
Periodic homogenization for inertial particles.
Physica D, 204 (3-4), 161-187, (2005).

05-08: Charles M. Elliott, S. A. McBeth
Analysis of the TV Regularization and H1 Fidelity Model for Decomposing an Image into Cartoon plus Texture
accepted for publication in Comm. Pure Appl. Analysis

05-07: Charles M. Elliott, Yohei Kashima
A Finite Element Analysis of Critical State Models for Type-II Superconductivity in 3D
IMA J. Numer. Anal. 27 (2007), 293-331.

05-06: John W. Barrett, Harald Garcke, Robert Nuernberg
A Phase Field Model for the Electromigration of Intergranular Voids
Interfaces and Free Boundaries 9 (2007), 171-210.

05-05: Markos A. Katsoulakis, Petr Plechac, Alexandros Sopasakis
Error Analysis Of Coarse-Grained Kinetic Monte Carlo Method
arXiv.org/math.NA/0509228P, 2005

05-04: Klaus Deckelnick,Gerhard Dziuk,Charles M. Elliott
Computation of Geometric Partial Differential Equations and Mean Curvature Flow
Acta Numerica 14 (2005), 139-232

05-03: D. Kay, R. Welford
A Multigrid Finite Element Solver for the Cahn-Hilliard Equation
J. Comp. Phys. 212 (2006), 288-304.

05-02: A. L.-S. Chua, C. A. Haselwandter, C. Baggio, and D. D. Vvedensky
Langevin Equations for Fluctuating Surfaces
submitted to Physical Review E

05-01: C. A. Haselwandter, D. D. Vvedensky
From Atomistic to Continuum Descriptions of Morphological Evolution
in Modeling of Morphological Evolution at Surfaces and Interface, edited by J. Evans, C. Orme, M. Asta, and Z. Zhang, Materials Research Society Symposium Proceedings, Vol. 859E (2005), pp. JJ8.8.1-JJ8.8.6.

2004

04-14: J. W. Barrett, X. Feng, A. 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.

04-13: J. W. Barrett, R. Nuernberg, M.R.E. Warner
Finite element approximation of soluble surfactant spreading on a thin film.
SIAM J. Numer. Anal. 44 (2006), 1218-1247.

04-12: J. W. Barrett, L. Prigozhin,
Dual formulations in critical state problems.
Interfaces and Free Boundaries 8 (2006), 347-368.

04-11: J. W. Barrett, J. Guidice, E. Suli
A posteriori error analysis of mixed finite element approximations to quasi-Newtonian inc ompressible flows

04-10: A. Cangiani, E. Suli
A-posteriori error estimators and RFB

04-09: C. Ortner
$\Gamma$-Limits of Galerkin Discretizations with Quadrature

04-08: R Kupferman, D. Givon, Andrew M Stuart
Extracting Macroscopic Dynamics: Model Problems and Algorithms

04-07: D. D. Vvedensky
Multiscale modelling of nanostructures
J. of Physics: Condensed Matter, 16, R1537-R1576 (2004).

04-06: John W. Barrett, Christoph Schwab, Endre Süli
Existence of global weak solutions for some polymeric flow models
M3AS 15 (2005), 939-983.

04-05: Markos A. Katsoulakis, Petr Plechac, Dimitrios K. Tsagkarogiannis
Mesoscopic modeling for continuous spin lattice systems: Model problems and micromagnetics application.
J. Stat. Phys. 119 (2005), No:1-2, pp 347-389.

04-04: John W. Barrett, Harald Garcke, Robert Nuernberg
Finite Element Approximation of a Phase Field Model for Surface Diffusion of Voids in a Stressed Solid
Math. Comp. 75 (2006), 7-41.

04-03: Raz Kupferman , Grigorios A. Pavliotis, Andrew M. Stuart
Ito versus Stratonovich white noise limits for systems with inertia and colored multiplicative noise.

04-02: Grigorios A. Pavliotis, Andrew M. Stuart
White noise limits for inertial particles in a random field.

04-01: Markos A. Katsoulakis, Petr Plechac
Equilibrium statistical measures in micromagnetics