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Numerical analysis of convection-diffusion-reaction problems with higher order characteristics/finite elements. I: Time discretization. (English) Zbl 1126.65080

This paper deals with the higher-order characteristics time discretization scheme for a convection-diffusion-reaction equation with mixed Dirichlet-Robin boundary conditions. The diffusive coefficient is variable and the velocity field is not necessarily divergence free. Under not very restrictive hypotheses on the data, the l (L 2 ) stability is proved and l (L 2 ) error estimates of order O(Δt 2 ) are obtained.

[For part II see ibid. 44, No. 5, 1854–1876 (2006; Zbl 1126.65081), reviewed below.]


MSC:
65M12Stability and convergence of numerical methods (IVP of PDE)
65M25Method of characteristics (IVP of PDE, numerical methods)
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
65M15Error bounds (IVP of PDE)
35K57Reaction-diffusion equations