Iterates of Volterra operators and indeterminate forms.

Braz e Silva, Pablo; Papa, Andrés R.R.

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This paper is devoted to the study of a posteriori error estimates for the scalar nonlinear convection-diffusion-reaction equation $c_{t} + \nabla \cdot (𝐮 f (c)) - \nabla \cdot (D \nabla c) + λ c = 0$ . The estimates for the error between the exact solution and an upwind finite volume approximation to the solution are derived in the $L^{1}$ -norm, independent of the diffusion parameter $D$ . The resulting a posteriori error estimate is used to define an grid adaptive solution algorithm for the finite volume scheme. Finally numerical experiments underline the applicability...