The research is focused on qualitative and numerical aspects in the field of the dynamics modeling of curvature driven flows of plane closed curves. We also focus on the study of various nonlocal geometric flows preserving geometric quantities, such as area or length. Special attention is paid to the design of numerical schemes that are optimal in terms of discretization points distribution on evolving varieties. Finally, we study applications in the field of phase interface dynamics and dislocation loops in materials research.
M. Remešíková, K. Mikula, P. Sarkoci and D. Ševčovič: Manifold evolution with tangential redistribution of points, SIAM J. Sci. Comput. 36-4 (2014), A1384-A1414.
M. Kolář, M. Beneš, D. Ševčovič: Area Preserving Geodesic Curvature Driven Flow of Closed Curves on a Surface, Discrete and Continuous Dynamical Systems - Series B, 22(10) 2017, 3671-3689.
D. Ševčovič and S.Yazaki: Computational and qualitative aspects of motion of plane curves with a curvature adjusted tangential velocity, Mathematical Methods in the Applied Sciences, 35(15) (2012), 1784-1798.
M. Kolář, M. Beneš, D. Ševčovič: Computational Analysis of the Conserved Mean-Curvature Flow for Open and Closed Curves in the Plane, Mathematics and Computers in Simulation, 126 2016, 1-13.
D. Ševčovič and S.Yazaki: Evolution of plane curves with a curvature adjusted tangential velocity, Japan J. Indust. Appl. Math., 28(3) (2011), 413-442.
K. Mikula, D. Ševčovič, M. Balažovjech: A simple, fast and stabilized flowing finite volume method for solving general curve evolution equations, Commun. Comput. Phys., 7(1) (2010), 195-211.
H. Garcke, Y. Kohsaka and D. Ševčovič: Nonlinear stability of stationary solutions for curvature flow with triple junction, Hokkaido Mathematical Journal, 38(4) (2009), 721-769.
V. Klement, T. Oberhuber and D. Ševčovič: Application of the level-set model with constraints in image segmentation, Numerical Mathematics, Theory, Methods and Applications, 9(1) 2016, 147-168.