@Article{CiCP-7-1,
author = {Mikula, Karol and Ševčovič, Daniel and Martin, Balažovjech},
title = {A Simple, Fast and Stabilized Flowing Finite Volume Method for Solving General Curve Evolution Equations},
journal = {Communications in Computational Physics},
year = {2010},
volume = {7},
number = {1},
pages = {195--211},
abstract = {<p style="text-align: justify;">A new simple Lagrangian method with favorable stability and efficiency
properties for computing general plane curve evolutions is presented. The method
is based on the flowing finite volume discretization of the intrinsic partial differential
equation for updating the position vector of evolving family of plane curves. A curve
can be evolved in the normal direction by a combination of fourth order terms related
to the intrinsic Laplacian of the curvature, second order terms related to the curvature,
first order terms related to anisotropy and by a given external velocity field. The
evolution is numerically stabilized by an asymptotically uniform tangential redistribution
of grid points yielding the first order intrinsic advective terms in the governing
system of equations. By using a semi-implicit in time discretization it can be numerically
approximated by a solution to linear penta-diagonal systems of equations (in
presence of the fourth order terms) or tri-diagonal systems (in the case of the second
order terms). Various numerical experiments of plane curve evolutions, including, in
particular, nonlinear, anisotropic and regularized backward curvature flows, surface
diffusion and Willmore flows, are presented and discussed.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.2009.08.169},
url = {https://global-sci.com/article/80973/a-simple-fast-and-stabilized-flowing-finite-volume-method-for-solving-general-curve-evolution-equations}
}