Numerical Simulation of Anisotropic Mean Curvature of Graphs in Relative Geometry

作者：Hoang Dieu Hung^*; Benes Michal; Oberhuber Tomas

来源：Acta Polytechnica Hungarica, 2013, 10(7): 99-115.

• anisotropy
• mean curvature
• Finsler geometry
• method of lines
• FDM

The aim of this paper is the numerical simulation of anisotropic mean curvature of graphs in the context of relative geometry, developed in [1]. We extend results in [4] to our problem; we prove an existence theorem and energy equality. The numerical scheme is based on the method of lines where the spatial derivatives are approximated by finite differences [2]. We then solve the resulting ODE system by means of the adaptive Runge-Kutta-Merson method. To show the stability of the scheme we prove the discrete version of the energy equality. Finally, we show experimental order of convergence and results of numerical experiments with various anisotropy settings.

• 出版日期2013