A phase field approach in the numerical study of the elastic bending energy for vesicle membranes

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A phase field formulation of the Willmore problem (2005, background): “velocity and electric fields, to ultimately extend the work in [1] to model membrane dynamics in electro-rheological fluids.”
A new phase-field model for strongly anisotropic systems (2009, methodology): “…construct phase-field approximations for the Willmore energy date back to De Giorgi (1991), who conjectured an appropriate approximation, which has since been analysed and simplified using different methods by Loreti & March (2000), Du et al. (2004, 2005), Röger & Schätzle (2006) and Wang (2007).”
The phase field method for geometric moving interfaces and their numerical approximations (2019, positive): “Given the complexities involved in these systems, effective numerical algorithms such as those utilizing high order spectral methods and adaptive discretizations [155, 161] and energy law preserving schemes [264] can be very useful for large scale and long time simulations.”
Error analysis of stabilized semi-implicit method of Allen-Cahnequation (2009, neutral): “[4, 5, 6, 9, 18, 19, 20]).”
The phase field technique for modeling multiphase materials (2008, background): “Effects of the elastic bending energy on the static deformation of a vesicle membrane were investigated in [298, 299].”