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

Bermúdez, Alfredo; Nogueiras, Maria R.; Vázquez, Carlos

SIAM J. Numer. Anal. 44, No. 5, 1829-1853 (2006).

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.]

Reviewer: Marius Ghergu (Dublin)

MSC:

65M12	Stability and convergence of numerical 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
65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M15	Error bounds for initial value and initial-boundary value problems involving PDEs
35K57	Reaction-diffusion equations

Keywords:

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

Citations:

Zbl 1126.65081