Griebel, Michael; Schweitzer, Marc Alexander A particle-partition of unity method. II: Efficient cover construction and reliable integration. (English) Zbl 1011.65069 SIAM J. Sci. Comput. 23, No. 5, 1655-1682 (2002). This work is a sequel to the authors’ paper [ibid. 22, No. 3, 853-890 (2000; Zbl 0974.65090)] where they introduced the implementation of a meshless partition of unity method for convection diffusion equation. In the present paper the cover construction and its interplay with the numerical integration problems in a Galerkin framework is treated in some detail. A hierarchical cover construction is advocated to increase the overall complexity of the method. Reviewer: Thomas Sonar (Braunschweig) Cited in 2 ReviewsCited in 50 Documents MSC: 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs 35K15 Initial value problems for second-order parabolic equations 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 35L15 Initial value problems for second-order hyperbolic equations 35J25 Boundary value problems for second-order elliptic equations Keywords:meshfree method; partition of unity; Galerkin discretization; convergence; numerical examples; meshless partition of unity method; convection-diffusion equation Citations:Zbl 0974.65090 PDFBibTeX XMLCite \textit{M. Griebel} and \textit{M. A. Schweitzer}, SIAM J. Sci. Comput. 23, No. 5, 1655--1682 (2002; Zbl 1011.65069) Full Text: DOI