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

Yusuke Imoto

    Research output: Contribution to journalArticlepeer-review

    1 Citation (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)33-43
    Number of pages11
    JournalApplications of Mathematics
    Volume64
    Issue number1
    DOIs
    Publication statusPublished - 2019 Feb 1

    Keywords

    • 65M12
    • Poisson equation
    • discrete Sobolev norm
    • generalized particle method
    • stability
    • unique solvability

    ASJC Scopus subject areas

    • Applied Mathematics

    Fingerprint

    Dive into the research topics of 'Unique solvability and stability analysis of a generalized particle method for a Poisson equation in discrete Sobolev norms'. Together they form a unique fingerprint.

    Cite this