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

Angela HandlovičováKarol Mikula — 2008

Applications of Mathematics

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.

Applications of approximate gradient schemes for nonlinear parabolic equations

Robert EymardAngela HandlovičováRaphaèle HerbinKarol MikulaOlga Stašová — 2015

Applications of Mathematics

We develop gradient schemes for the approximation of the Perona-Malik equations and nonlinear tensor-diffusion equations. We prove the convergence of these methods to the weak solutions of the corresponding nonlinear PDEs. A particular gradient scheme on rectangular meshes is then studied numerically with respect to experimental order of convergence which shows its second order accuracy. We present also numerical experiments related to image filtering by time-delayed Perona-Malik and tensor diffusion...

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