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Applications of Mathematics

, Volume 64, Issue 1, pp 33–43 | Cite as

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

  • Yusuke ImotoEmail author
Article

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 general- ized 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 solv- ability 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.

Keywords

generalized particle method Poisson equation unique solvability stability discrete Sobolev norm 

MSC 2010

65M12 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2019

Authors and Affiliations

  1. 1.Tohoku Forum for CreativityTohoku UniversitySendaiJapan

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