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

Angela Handlovičová; Karol Mikula

Applications of Mathematics (2008)

  • Volume: 53, Issue: 2, page 105-129
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Handlovičová, Angela, and Mikula, Karol. "Stability and consistency of the semi-implicit co-volume scheme for regularized mean curvature flow equation in level set formulation." Applications of Mathematics 53.2 (2008): 105-129. <http://eudml.org/doc/33313>.

@article{Handlovičová2008,
abstract = {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.},
author = {Handlovičová, Angela, Mikula, Karol},
journal = {Applications of Mathematics},
keywords = {mean curvature flow; level set equation; numerical solution; semi-implicit scheme; complementary volume method; unconditional stability; consistency; mean curvature flow; level set equation; numerical solution; semi-implicit scheme; complementary volume method},
language = {eng},
number = {2},
pages = {105-129},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Stability and consistency of the semi-implicit co-volume scheme for regularized mean curvature flow equation in level set formulation},
url = {http://eudml.org/doc/33313},
volume = {53},
year = {2008},
}

TY - JOUR
AU - Handlovičová, Angela
AU - Mikula, Karol
TI - Stability and consistency of the semi-implicit co-volume scheme for regularized mean curvature flow equation in level set formulation
JO - Applications of Mathematics
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 2
SP - 105
EP - 129
AB - 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.
LA - eng
KW - mean curvature flow; level set equation; numerical solution; semi-implicit scheme; complementary volume method; unconditional stability; consistency; mean curvature flow; level set equation; numerical solution; semi-implicit scheme; complementary volume method
UR - http://eudml.org/doc/33313
ER -

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