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Handlovičová, Angela; Mikula, Karol

Stability and consistency of the semi-implicit co-volume scheme for regularized mean curvature flow equation in level set formulation. (English) Zbl 1199.35197

Appl. Math., Praha 53, No. 2, 105-129 (2008).
Summary: We show stability and consistency of the linear semi-implicit complementary volume numerical scheme for solving the regularized, in the sense of L. C. Evans and J. 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.

Cited in 3 Documents

MSC:

35K93 Quasilinear parabolic equations with mean curvature operator
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs

Keywords:

mean curvature flow; level set equation; numerical solution; semi-implicit scheme; complementary volume method
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\textit{A. Handlovičová} and \textit{K. Mikula}, Appl. Math., Praha 53, No. 2, 105--129 (2008; Zbl 1199.35197)
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