A Residual a Posteriori Error Estimators for a Model for Flow in Porous Media with Fractures

Frédéric Hecht 1, 2 I. Naji 3 Z. Mghazli 3 Jean Roberts 4
1 ALPINES - Algorithms and parallel tools for integrated numerical simulations
INSMI - Institut National des Sciences Mathématiques et de leurs Interactions, Inria de Paris, LJLL - Laboratoire Jacques-Louis Lions
Abstract : This article is concerned with a posteriori error estimates for a discrete-fracture, multidimensional, numerical model for flow in a fractured porous medium. Local residual error estimators are defined and upper and lower bounds in terms of these estimators for both the pressure and the Darcy velocity are derived. Numerical examples using these estimates for automatic grid refinement are given. Keywords A posteriori error estimate · mixed finite element · reduced model · fractured porous media.
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Frédéric Hecht, I. Naji, Z. Mghazli, Jean Roberts. A Residual a Posteriori Error Estimators for a Model for Flow in Porous Media with Fractures. Journal of Scientific Computing, Springer Verlag, 2018, pp 1-34. ⟨10.1007/s10915-018-0875-7⟩. ⟨hal-01972116⟩

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