Geodesic
Unique solvability and stability analysis of a generalized particle method for a Poisson equation in discrete Sobolev norms
Applications of Mathematics, Tome 64 (2019) no. 1, pp. 33-43.

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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.
DOI : 10.21136/AM.2019.0210-18
Classification : 65M12, 65N12, 65N75
Keywords: generalized particle method; Poisson equation; unique solvability; stability; discrete Sobolev norm 
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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, Tome 64 (2019) no. 1, pp. 33-43. doi : 10.21136/AM.2019.0210-18. http://geodesic.mathdoc.fr/articles/10.21136/AM.2019.0210-18/

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