×

A particle-partition of unity method. II: Efficient cover construction and reliable integration. (English) Zbl 1011.65069

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.

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

Citations:

Zbl 0974.65090
PDFBibTeX XMLCite
Full Text: DOI