Applications of Mathematics, Vol. 64, No. 1, pp. 33-43, 2019

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

Yusuke Imoto

Received August 2, 2018.   Published online January 7, 2019.

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.
Keywords:  generalized particle method; Poisson equation; unique solvability; stability; discrete Sobolev norm
Classification MSC:  65M12
DOI:  10.21136/AM.2019.0210-18

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Affiliations:   Yusuke Imoto, Tohoku Forum for Creativity, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan, e-mail:

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