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.
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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: y-imoto@tohoku.ac.jp
