Abstract
We propose a finite element algorithm for computing the motion of a surface moving by mean curvature. The algorithm uses the level set formulation so that changes in topology of the surface can be accommodated. Stability is deduced by showing that the discrete solutions satisfy both $L^\infty $ and $W^{1.1} $ bounds. Existence of discrete solutions and connections with Brakke flows are established. Some numerical examples and application to related problems, such as the phase field equations, are also presented.
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