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Stability and consistency of the semi-implicit co-volume scheme for regularized mean curvature flow equation in level set formulation

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Abstract

We show stability and consistency of the linear semi-implicit complementary volume numerical scheme for solving the regularized, in the sense of Evans and Spruck, mean curvature flow equation in the level set formulation. The numerical method is based on the finite volume methodology using the so-called complementary volumes to a finite element triangulation. The scheme gives the solution in an efficient and unconditionally stable way.

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Authors and Affiliations

  1. Department of Mathematics, Slovak University of Technology, Radlinského 11, 813 68, Bratislava, Slovakia

    Angela Handlovičová & Karol Mikula

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  1. Angela Handlovičová
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  2. Karol Mikula
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Correspondence to Angela Handlovičová.

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Handlovičová, A., Mikula, K. Stability and consistency of the semi-implicit co-volume scheme for regularized mean curvature flow equation in level set formulation. Appl Math 53, 105–129 (2008). https://doi.org/10.1007/s10492-008-0015-z

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  • DOI: https://doi.org/10.1007/s10492-008-0015-z

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