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A particle-partition of unity method for the solution of elliptic, parabolic, and hyperbolic PDEs. (English) Zbl 0974.65090
The particle-partition of unity method is a generalized partition of unity method. The present paper discusses the details of the method in case of convection-diffusion equations where the method of characteristics and an operator splitting approach is employed to take care of the distinguished features of the equations. The method can be used in an \(h\)- or \(p\)-adaptive strategy and owes much to the partition of unity finite element method regarding the convergence behaviour. Numerical results are given.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical 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
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
35L15 Initial value problems for second-order hyperbolic equations
35J25 Boundary value problems for second-order elliptic equations
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PLTMG; UG
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