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Computation of geometric partial differential equations and mean curvature flow. (English) Zbl 1113.65097
A review of the computation of curvature-dependent motion of interfaces by means of geometric partial differential equations is given. The classical problem of finding a surface evolving everywhere with respect to a normal velocity given by mean curvature is adressed and many possible approaches are discussed thoroughly. The level set method and the phase field method and their analysis is presented and numerical examples are given throughout.

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
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