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Mathematical analysis of a discrete fracture model coupling Darcy flow in the matrix with Darcy-Forchheimer flow in the fracture
We consider a model for flow in a porous medium with a fracture in which the
flow in the fracture is governed by the Darcy-Forchheimer law while that in the
surrounding matrix is governed by Darcy's law. We give an appropriate mixed,
variational formulation and show existence and uniqueness of the solution. To
show existence we give an analogous formulation for the model in which the
Darcy-Forchheimer law is the governing equation throughout the domain. We show
existence and uniqueness of the solution and show that the solution for the
model with Darcy's law in the matrix is the weak limit of solutions of the
model with the Darcy-Forchheimer law in the entire domain when the Forchheimer
coefficient in the matrix tends toward zero
Finite element approximation of the transport of reactive solutes in porous media .1. Error estimates for nonequilibrium adsorption processes
Published versio
An improved error bound for a Lagrange-Galerkin method for contaminant transport with non-Lipschitzian adsorption kinetics
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