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Zbl 1126.65080
Bermúdez, Alfredo; Nogueiras, Maria R.; Vázquez, Carlos
Numerical analysis of convection-diffusion-reaction problems with higher order characteristics/finite elements. I: Time discretization. (English)
[J] SIAM J. Numer. Anal. 44, No. 5, 1829-1853 (2006). ISSN 0036-1429; ISSN 1095-7170/e

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 $l^\infty(L^2)$ stability is proved and $l^\infty(L^2)$ error estimates of order $O(\Delta t^2)$ are obtained. [For part II see ibid. 44, No.~5, 1854--1876 (2006; Zbl 1126.65081), reviewed below.]
[Marius Ghergu (Dublin)]

MSC 2000:: *65M12 Stability and convergence of numerical methods (IVP of PDE)
65M25 Method of characteristics (numerical)
65M60 Finite numerical methods (IVP of PDE)
65M15 Error bounds (IVP of PDE)
35K57 Reaction-diffusion equations

Keywords: convection-diffusion-reaction equation; characteristics method; stability; finite elements; error estimates

Citations: Zbl 1126.65081

Cited in: Zbl 1126.65081

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