Nonequilibrium Interface Dynamics:
Hierarchical Modeling and Multiscale Simulation of Materials Interfaces

CSIC Building (#406), Seminar Room 4122.
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Finite Element Methods for Surface Diffusion

Dr. Ricardo H. Nochetto

University of Maryland

Abstract:   Surface diffusion is a 4th order (highly nonlinear) geometric driven motion of a surface with normal velocity proportional to the surface Laplacian of mean curvature. We present a novel variational formulation for parametric surfaces which is semi-implicit, requires no explicit parametrization, and yields a linear system of lower order elliptic PDE to solve at each time step. We develop a finite element method, and propose a Schur complement approach to solve the resulting linear systems. We also introduce a new graph formulation and show stability and optimal a priori error estimates for position and curvature. We illustrate both approaches with several simulations of curves and surfaces, some exhibiting singularites (such as pinch-off and crack formation) in finite time. The beneficial use of mesh smoothing, which helps prevent mesh distortion, and space-time adaptivity is also addressed.