Publications

Journal Articles

[27] Convergence of a scheme for elastic flow with tangential mesh movement
(with P Pozzi), ESAIM: Mathematical Modelling and Numerical Analysis, accepted.

[26] On the sharp interface limit of a phase field model for near spherical two phase biomembranes
(with C Elliott, L Hatcher), Interf. Free Bound., accepted.

[25] On motion by curvature of a network with a triple junction
(with P Pozzi), SMAI J. Comp. Math. 7 (2021), 27–55.

[24] A finite element method for a fourth order surface equation with application to the onset of cell blebbing
(with A Dedner, A Nixon), Frontiers Appl. Math. Stat. 6 (2020).

[23] Mathematical modelling in cell migration: tackling biochemistry in changing geometries
(with T Bretschneider), Biochem. Soc. Trans. 48 (2020), 419–428.

[22] Phase field modelling of surfactants in multiphase flow
(with O Dunbar, K Lam), Interf. Free Bound. 21 (2019), 495–547.

[21] Elastic flow interacting with a lateral diffusion process: The one-dimensional graph case
(with P Pozzi), IMA J Numer Analysis 39 (2019), 201–234. (preprint)

[20] Curve shortening flow coupled to lateral diffusion
(with P Pozzi), Numerische Mathematik 135 (2017), 1171--1205. (paper) (preprint)

[19] Analysis of the diffuse domain approach for a bulk-surface coupled PDE system
(with H Abels and K Lam), SIAM J Math Analysis 47 (2015), 3687--3725. (preprint)

[18] On some linear parabolic PDEs on moving hypersurfaces
(with A Alphonse and C Elliott), Interfaces Free Bound 17 (2015), 157--187.

[17] Parameter Identification Problems in the Modelling of Cell Motility
(with W Croft, C Elliott, G Ladds, C Venkataraman, C Weston), J Math Biol 71 (2015), 399--436. (preprint)

[16] Higher Order Discontinuous Galerkin Methods on Surfaces
(with P Antonietti, A Dedner, P Madhavan, S Stangalino, and M Verani), SIAM J Numer Analysis 53 (2015), 1145--1171. (preprint)

[15] An Abstract Framework for Parabolic PDEs on Evolving Spaces
(with A Alphonse and C Elliott), Portugal Math 72 (2015), 1--46. (preprint)

[14] Diffuse Interface Modelling of Soluble Surfactants in Two-Phase Flow
(with H Garcke and K Lam), Commun Math Sci 12 (2014), 1475--1522. (preprint)

[13] Analysis of the discontinuous Galerkin method for elliptic problems on surfaces
(with A Dedner and P Madhavan), IMA J Numer Analysis 33 (2013), 952--973. (preprint)

[12] Modelling cell motility and chemotaxis with evolving surface finite elements
(with C Elliott, C Venkataraman), J Roy Soc Interface 9 (2012), 3027--3044. (preprint)

[11] Computation of two-phase biomembranes with phase dependent material parameters using surface finite elements
(with C Elliott), Commun Comput Phys 13 (2013), 325--360. (preprint)

[10] Numerical computation of advection and diffusion on evolving diffuse interfaces
(with C Elliott, V Styles, and R Welford), IMA J Numer Analysis 31 (2011), 786--812. (preprint)

[9] A surface phase field model for two-phase biological membranes
(with C Elliott), SIAM J Appl Math 70 (2010), 2904--2928. (preprint)

[8] Modeling and computation of two phase geometric biomembranes using surface finite elements
(with C Elliott), J Comput Phys 229 (2010), 6585--6612. (preprint)

[7] Analysis of a diffuse interface approach to an advection diffusion equation on a moving surface
(with C Elliott), Math Models Methods Appl Sci 19 (2009), 787--802. (preprint)

[6] Phase-field model for multiphase systems with preserved volume fractions
(with B Nestler, F Wendler, M Selzer, and H Garcke), Phys Rev E 78 (2008), 011604-1--7.

[5] Allen-Cahn systems with volume constraints
(with H Garcke, B Nestler, and F Wendler), Math Models Methods Appl Sci 18 (2008), 1347--1381. (preprint)

[4] Weak solutions to a multi-phase field system of parabolic equations related to alloy solidification
Adv Math Sc Appl 17 (2007), 589--638. (preprint)

[3] Second order phase field asymptotics for multi-component systems
(with H Garcke), Interfaces Free Bound 8 (2006), 131--157. (preprint)

[2] Multicomponent alloy solidification: Phase-field modeling and simulations
(with B Nestler and H Garcke), Phys Rev E 71 (2005), 041609-1--6. (preprint)

[1] A diffuse interface model for alloys with multiple components and phases
(with H Garcke and B Nestler) SIAM J Appl Math 64 (2004), 775--799. (preprint)

Articles in Proceedings and Reports

  • On a diffuse interface approach to PDEs on surfaces and networks
    Oberwolfach Report (2019).

  • On a surface finite element method for cell blebbing
    (with A Nixon), Oberwolfach Report (2019).

  • Diffuse interface approach to PDEs on clusters and networks with applications to surfactants in multi-phase flow
    (with O Dunbar), in Geometric PDEs: Surface and Bulk Processes, Oberwolfach Report (2015).

  • Phase-field modelling of two-phase flow with soluble surfactant
    (with H Garcke and K Lam), in Interfaces and Free Boundaries: Analysis, Control and Simulation, Oberwolfach Report, doi: 10.4171/OWR/2013/15 (2013).

  • H1 Willmore flow with local area preservation
    in Geometric Partial Differential Equations: Theory, Numerics and Applications, Oberwolfach Report 8 (2011), 3077--3144.

  • Lateral phase separation on biomembranes
    (with C Elliott), in Mathematics of Biological Membranes, Oberwolfach Report 5 (2008), 2293--2336.

  • Multi-phase field systems with anisotropic surface energies
    Proc Appl Math Mech 19 (2007), 1150101--1150102.

  • Elastic biomembranes with lateral phase separation
    (with C Elliott), in Phase Transitions, Oberwolfach Report 4 (2007), 1575--1650.

  • Phase field modelling of alloy solidification
    (with H Garcke and B Nestler), in Control of Free Boundaries, Oberwolfach Report 4 (2007), 447--468.

  • Multiscale Problems in Solidification Processes
    (with C Eck and H Garcke) in Analysis, Modeling and Simulation of Multiscale Problems, edt. A Mielke (2006), 21--64. (preprint)

  • Surface energies in multi phase systems with diffuse phase boundaries
    Int Ser Num Math 154 (2006), 413--423. (preprint)

  • On phase field modelling of solidification
    (with H Garcke and B Nestler), in Phasenübergänge, Oberwolfach Report 1 (2004), 1587--1656.

  • A phase field model for the solidification process of multicomponent alloys
    (with H Garcke and B Nestler) in Interface and Transport Dynamics, edt H Emmerich, B Nestler, and M Schreckenberg, Lecture Notes in Computational Science and Engineering 32 (2003), 142-149.

    • Preprints


  • Solving reaction-diffusion equations on evolving surfaces defined by biological image data
    (with T Bretschneider, C Elliott, B Stinner, T Ranner), submitted. (preprint)

  • The Cahn-Hilliard equation on an evolving surface
    (with D O'Connor). (preprint)

    • Theses

  • Derivation and Analysis of a Phase Field Model for Alloy Solidification
    doctoral thesis, Universität Regensburg, Germany (2005). (electronic version)

  • Geometrisches Wachstum durch kristalline Krümmung: Dreifachknotenpunkte und selbstähnliche Bewegungen
    diploma thesis, Universität Bonn, Germany (2001).

  • Méthode de Godounov pour une loi de conservation scalaire
    TER (travail d´étude et de recherche), Université Joseph Fourier (Grenoble 1), France (2000).

  • Travail pratique sur la méthode des éléments finis
    (with C. Jost), Université Joseph Fourier (Grenoble 1), France (2000).


    • BSt