DISCRETIZATION OF AN UNSTEADY FLOW THROUGH A POROUS SOLID MODELED BY DARCY'S EQUATIONS
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The system of unsteady Darcy's equations considered here models the time-dependent flow of an incompressible fluid such as water in a rigid porous medium. We propose a discretization of this problem that relies on a backward Euler's scheme for the time variable and finite elements for the space variables. We prove a priori error estimates that justify the optimal convergence properties of the discretization and a posteriori error estimates that allow for an efficient adaptivity strategy both for the time steps and the meshes. © 2008 World Scientific Publishing Company.
author list (cited authors)
BERNARDI, C., GIRAULT, V., & RAJAGOPAL, K. R.