Construction of convergent adaptive weighted essentially non-oscillatory schemes for Hamilton-Jacobi equations on triangular meshes

Kwangil Kim; Unhyok Hong; Kwanhung Ri; Juhyon Yu

Applications of Mathematics (2021)

  • Volume: 66, Issue: 4, page 599-617
  • ISSN: 0862-7940

Abstract

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We propose a method of constructing convergent high order schemes for Hamilton-Jacobi equations on triangular meshes, which is based on combining a high order scheme with a first order monotone scheme. According to this methodology, we construct adaptive schemes of weighted essentially non-oscillatory type on triangular meshes for nonconvex Hamilton-Jacobi equations in which the first order monotone approximations are occasionally applied near singular points of the solution (discontinuities of the derivative) instead of weighted essentially non-oscillatory approximations. Through detailed numerical experiments, the convergence and effectiveness of the proposed adaptive schemes are demonstrated.

How to cite

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Kim, Kwangil, et al. "Construction of convergent adaptive weighted essentially non-oscillatory schemes for Hamilton-Jacobi equations on triangular meshes." Applications of Mathematics 66.4 (2021): 599-617. <http://eudml.org/doc/297936>.

@article{Kim2021,
abstract = {We propose a method of constructing convergent high order schemes for Hamilton-Jacobi equations on triangular meshes, which is based on combining a high order scheme with a first order monotone scheme. According to this methodology, we construct adaptive schemes of weighted essentially non-oscillatory type on triangular meshes for nonconvex Hamilton-Jacobi equations in which the first order monotone approximations are occasionally applied near singular points of the solution (discontinuities of the derivative) instead of weighted essentially non-oscillatory approximations. Through detailed numerical experiments, the convergence and effectiveness of the proposed adaptive schemes are demonstrated.},
author = {Kim, Kwangil, Hong, Unhyok, Ri, Kwanhung, Yu, Juhyon},
journal = {Applications of Mathematics},
keywords = {Hamilton-Jacobi equation; first order monotone scheme; high order scheme; weighted essentially non-oscillatory scheme; adaptive scheme; convergence},
language = {eng},
number = {4},
pages = {599-617},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Construction of convergent adaptive weighted essentially non-oscillatory schemes for Hamilton-Jacobi equations on triangular meshes},
url = {http://eudml.org/doc/297936},
volume = {66},
year = {2021},
}

TY - JOUR
AU - Kim, Kwangil
AU - Hong, Unhyok
AU - Ri, Kwanhung
AU - Yu, Juhyon
TI - Construction of convergent adaptive weighted essentially non-oscillatory schemes for Hamilton-Jacobi equations on triangular meshes
JO - Applications of Mathematics
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 4
SP - 599
EP - 617
AB - We propose a method of constructing convergent high order schemes for Hamilton-Jacobi equations on triangular meshes, which is based on combining a high order scheme with a first order monotone scheme. According to this methodology, we construct adaptive schemes of weighted essentially non-oscillatory type on triangular meshes for nonconvex Hamilton-Jacobi equations in which the first order monotone approximations are occasionally applied near singular points of the solution (discontinuities of the derivative) instead of weighted essentially non-oscillatory approximations. Through detailed numerical experiments, the convergence and effectiveness of the proposed adaptive schemes are demonstrated.
LA - eng
KW - Hamilton-Jacobi equation; first order monotone scheme; high order scheme; weighted essentially non-oscillatory scheme; adaptive scheme; convergence
UR - http://eudml.org/doc/297936
ER -

References

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