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Estimations a posteriori pour l'équation de convection-diffusion-réaction instationnaire et applications aux volumes finis

Abstract : We consider the time-dependent convection--diffusion--reaction equation. We derive a posteriori error estimates for the discretization of this equation by the cell-centered finite volume scheme in space and a backward Euler scheme in time. The estimates are established in the energy norm and they bound the error between the exact solution and a locally post processed approximate solution, based on $Hdiv$-conforming diffusive and convective flux reconstructions, as well as an $H^1_0(Omega)$-conforming potential reconstruction. We propose an adaptive algorithm which ensures the control of the total error with respect to a user-defined relative precision by refining the meshes adaptively while equilibrating the time and space contributions to the error. We also present numerical experiments. Finally, we derive another a posteriori error estimate in the energy norm augmented by a dual norm of the time derivative and the skew symmetric part of the differential operator. The new estimate is robust in convective-dominated regimes and local-in-time and global-in-space lower bounds are also derived
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Nancy Chalhoub. Estimations a posteriori pour l'équation de convection-diffusion-réaction instationnaire et applications aux volumes finis. Mathématiques générales [math.GM]. Université Paris-Est, 2012. Français. ⟨NNT : 2012PEST1065⟩. ⟨pastel-00794392⟩

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