Unique solvability and stability analysis of a generalized particle method for a Poisson equation in discrete Sobolev norms

Yusuke Imoto

Applications of Mathematics (2019)

  • Volume: 64, Issue: 1, page 33-43
  • ISSN: 0862-7940

Abstract

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Unique solvability and stability analysis is conducted for a generalized particle method for a Poisson equation with a source term given in divergence form. The generalized particle method is a numerical method for partial differential equations categorized into meshfree particle methods and generally indicates conventional particle methods such as smoothed particle hydrodynamics and moving particle semi-implicit methods. Unique solvability is derived for the generalized particle method for the Poisson equation by introducing a connectivity condition for particle distributions. Moreover, stability is obtained for the discretized Poisson equation by introducing discrete Sobolev norms and a semi-regularity condition of a family of discrete parameters.

How to cite

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Imoto, Yusuke. "Unique solvability and stability analysis of a generalized particle method for a Poisson equation in discrete Sobolev norms." Applications of Mathematics 64.1 (2019): 33-43. <http://eudml.org/doc/294216>.

@article{Imoto2019,
abstract = {Unique solvability and stability analysis is conducted for a generalized particle method for a Poisson equation with a source term given in divergence form. The generalized particle method is a numerical method for partial differential equations categorized into meshfree particle methods and generally indicates conventional particle methods such as smoothed particle hydrodynamics and moving particle semi-implicit methods. Unique solvability is derived for the generalized particle method for the Poisson equation by introducing a connectivity condition for particle distributions. Moreover, stability is obtained for the discretized Poisson equation by introducing discrete Sobolev norms and a semi-regularity condition of a family of discrete parameters.},
author = {Imoto, Yusuke},
journal = {Applications of Mathematics},
keywords = {generalized particle method; Poisson equation; unique solvability; stability; discrete Sobolev norm},
language = {eng},
number = {1},
pages = {33-43},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Unique solvability and stability analysis of a generalized particle method for a Poisson equation in discrete Sobolev norms},
url = {http://eudml.org/doc/294216},
volume = {64},
year = {2019},
}

TY - JOUR
AU - Imoto, Yusuke
TI - Unique solvability and stability analysis of a generalized particle method for a Poisson equation in discrete Sobolev norms
JO - Applications of Mathematics
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 1
SP - 33
EP - 43
AB - Unique solvability and stability analysis is conducted for a generalized particle method for a Poisson equation with a source term given in divergence form. The generalized particle method is a numerical method for partial differential equations categorized into meshfree particle methods and generally indicates conventional particle methods such as smoothed particle hydrodynamics and moving particle semi-implicit methods. Unique solvability is derived for the generalized particle method for the Poisson equation by introducing a connectivity condition for particle distributions. Moreover, stability is obtained for the discretized Poisson equation by introducing discrete Sobolev norms and a semi-regularity condition of a family of discrete parameters.
LA - eng
KW - generalized particle method; Poisson equation; unique solvability; stability; discrete Sobolev norm
UR - http://eudml.org/doc/294216
ER -

References

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  8. Ishijima, K., Kimura, M., 10.11540/jsiamt.20.3_165, Trans. Japan Soc. Ind. Appl. Math. 20 (2010), 165-182 Japanese. (2010) DOI10.11540/jsiamt.20.3_165
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