Parametric FEM for geometric biomembranes
Journal of Computational Physics
Modeling and computation of two phase geometric biomembranes using surface finite elements
Journal of Computational Physics
Geometrically Consistent Mesh Modification
SIAM Journal on Numerical Analysis
Higher-Order Feature-Preserving Geometric Regularization
SIAM Journal on Imaging Sciences
On a linear programming approach to the discrete willmore boundary value problem and generalizations
Proceedings of the 7th international conference on Curves and Surfaces
Mumford-Shah-Euler Flow with Sphere Constraint and Applications to Color Image Inpainting
SIAM Journal on Imaging Sciences
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We propose a new algorithm for the computation of Willmore flow. This is the L 2-gradient flow for the Willmore functional, which is the classical bending energy of a surface. Willmore flow is described by a highly nonlinear system of PDEs of fourth order for the parametrization of the surface. The spatially discrete numerical scheme is stable and consistent. The discretization relies on an adequate calculation of the first variation of the Willmore functional together with a derivation of the second variation of the area functional which is well adapted to discretization techniques with finite elements. The algorithm uses finite elements on surfaces. We give numerical examples and tests for piecewise linear finite elements. A convergence proof for the full algorithm remains an open question.