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On the transport-diffusion algorithm and its applications to the Navier-Stokes equations. (English) Zbl 0505.76100
Summary: This paper deals with an algorithm for the solution of diffusion and/or convection equations where we mixed the method of characteristics and the finite element method. Globally it looks like one does one step of transport plus one step of diffusion (or projection) but the mathematics show that it is also an implicit time discretization of the PDE in Lagrangian form. We give an error bound \((h+\Delta t+h\times h/\Delta t\) in the interesting case) that holds also for the Navier-Stokes equations even when the Reynolds number is infinite (Euler equation).

MSC:
76R99 Diffusion and convection
76M99 Basic methods in fluid mechanics
65M15 Error bounds 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
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35Q30 Navier-Stokes equations
82C70 Transport processes in time-dependent statistical mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
35Q05 Euler-Poisson-Darboux equations
Software:
SHASTA
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References:
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