A linear backward Euler scheme for a class of degenerate advection–diffusion equations: A mathematical analysis of the convergence in L∞(0, T0;L2(Ω)) and in L2(0, T0;H1(Ω))

Autor:	Koffi B. Fadimba
Rok vydání:	2014
Předmět:	Discretization Error analysis Advection Linearization Applied Mathematics Regularization (physics) Mathematical analysis Degenerate energy levels Saturation (chemistry) Backward Euler method Analysis Mathematics
Zdroj:	Analysis and Applications. 12:227-249
ISSN:	1793-6861 0219-5305
DOI:	10.1142/s0219530514500031
Popis:	This paper concerns itself with establishing convergence estimates for a linearized scheme for solving numerically the saturation equation. In a previous paper, error estimates were obtained for the same scheme in L2(0, T0;L2(Ω)). In this work, we establish error estimates for the linear scheme in L∞(0, T0;L2(Ω)) and in L2(0, T0;H1(Ω)) (in the discrete norms). Under certain realistic conditions, we show that, if the regularization parameter β and the spatial discretization parameter h are carefully chosen in terms of the time-stepping parameter Δt, the convergence, in these spaces, is at least of order O((Δt)α) for some determined α > 0, function of a parameter μ > 0 defined in the problem. Examples of possible choices of β and h in terms of Δt are given.
Databáze:	OpenAIRE
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