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Volume 21, Issue 4
Numerical Dissipation for Three-Point Difference Schemes to Hyperbolic Equations with Uneven Meshes

Zi-Niu Wu

J. Comp. Math., 21 (2003), pp. 519-534.

Published online: 2003-08

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  • Abstract

The widely used locally adaptive Cartesian grid methods involve a series of abruptly refined interfaces. The numerical dissipation due to these interfaces is studied here for three-point difference approximations of a hyperbolic equation. It will be shown that if the wave moves in the fine-to-coarse direction then the dissipation is positive (stabilizing), and if the wave moves in the coarse-to-fine direction then the dissipation is negative (destabilizing).

  • Keywords

Refined interfaces, Numerical dissipation, Three-point difference approximation, Hyperbolic equation.

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COPYRIGHT: © Global Science Press

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@Article{JCM-21-519, author = {Wu , Zi-Niu}, title = {Numerical Dissipation for Three-Point Difference Schemes to Hyperbolic Equations with Uneven Meshes}, journal = {Journal of Computational Mathematics}, year = {2003}, volume = {21}, number = {4}, pages = {519--534}, abstract = {

The widely used locally adaptive Cartesian grid methods involve a series of abruptly refined interfaces. The numerical dissipation due to these interfaces is studied here for three-point difference approximations of a hyperbolic equation. It will be shown that if the wave moves in the fine-to-coarse direction then the dissipation is positive (stabilizing), and if the wave moves in the coarse-to-fine direction then the dissipation is negative (destabilizing).

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10256.html} }
TY - JOUR T1 - Numerical Dissipation for Three-Point Difference Schemes to Hyperbolic Equations with Uneven Meshes AU - Wu , Zi-Niu JO - Journal of Computational Mathematics VL - 4 SP - 519 EP - 534 PY - 2003 DA - 2003/08 SN - 21 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10256.html KW - Refined interfaces, Numerical dissipation, Three-point difference approximation, Hyperbolic equation. AB -

The widely used locally adaptive Cartesian grid methods involve a series of abruptly refined interfaces. The numerical dissipation due to these interfaces is studied here for three-point difference approximations of a hyperbolic equation. It will be shown that if the wave moves in the fine-to-coarse direction then the dissipation is positive (stabilizing), and if the wave moves in the coarse-to-fine direction then the dissipation is negative (destabilizing).

Wu , Zi-Niu. (2003). Numerical Dissipation for Three-Point Difference Schemes to Hyperbolic Equations with Uneven Meshes. Journal of Computational Mathematics. 21 (4). 519-534. doi:
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