Thursday, October 6, 9:30 am in room MTH 3206, University of Maryland,
College Park
Convergence for a Finite Element Approximation of
Curvature Driven Interface Motion
Prof. Claudio Verdi
Department of Mathematics
University of Milan, Italy
We consider a curve which propagates in the normal direction with
velocity proportional to its curvature plus a forcing term.
This geometric problem is first approximated by a singularly
perturbed parabolic double obstacle problem with small parameter
epsilon>0 . Conforming piecewise linear finite elements over a
quasi-uniform and strongly acute mesh of size h are further
used for space discretization, and combined with backward
differences for time discretization with uniform time-step tau .
We show convergence and linear error estimates
for the zero level set of the fully discrete solution
to the true interface, even past singularities.
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