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Research interests

Geometric PDEs and Numerical Analysis

  • Intrinsic Flows: Ricci Flow, Harmonic Map Heat Flow
  • Extrinsic Flows: Mean Curvature Flow, Willmore Flow
  • Mesh improvement via reparametrizations based on the DeTurck trick
  • Application of geometric PDEs to cell biology



Publications

Preprints

  1. On the computation of harmonic maps by unconstrained algorithms based on totally geodesic embeddings, arXiv:1610.05276, 17 Oct 2016.

Journal articles

  1. with C. M. Elliott and G. Hobbs: Small deformations of Helfrich energy minimising surfaces with applications to biomembranes, Mathematical Models and Methods in Applied Sciences, Vol. 27, 8: 1547-1586, 2017.
  2. with C. M. Elliott: On algorithms with good mesh properties for problems with moving boundaries based on the Harmonic Map Heat Flow and the DeTurck trick, SMAI Journal of computational mathematics 2: 141-176, 2016.
  3. with C. M. Elliott: On Approximations of the Curve Shortening Flow and of the Mean Curvature Flow based on the DeTurck trick,
    IMA Journal of Numerical Analysis 2016; doi: 10.1093/imanum/drw020.
  4. with C. M. Elliott: Time-periodic solutions of advection-diffusion equations on moving hypersurfaces, SIAM Journal on Mathematical Analysis, Vol. 47, 3: 1693-1718, 2015.
  5. Numerical Ricci-DeTurck Flow, Numerische Mathematik, Vol. 131, 2: 241-271, 2015.
  6. Isoparametric finite element approximation of Ricci curvature, IMA J Numer Anal 33, 4: 1265-1290, 2013.
  7. with J. Ankerhold: Non-adiabatic transitions between adiabatic surfaces: Phase diffusion in superconducting atomic point contacts, Phys. Rev. B 80: 064502, 2009.

Proceedings and non-peer-reviewed publications

  1. with C. M. Elliott: On Approximations of the Curve Shortening and Mean Curvature flows based on the DeTurck trick, Oberwolfach Report No. 4/2016.
  2. with C. M. Elliott: On algorithms with good mesh properties based on the harmonic map heat flow and the DeTurck trick, Oberwolfach Report No. 55, 2015.
  3. Computation of Ricci curvature, Oberwolfach Report No. 54, 2011.
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