Gradient discretization of hybrid dimensional Darcy flows in fractured porous media
type: Item
instance of: scholarly article
title: Gradient discretization of hybrid dimensional Darcy flows in fractured porous media
zbMATH Open document ID: 1358.76069
author: Konstantin Brenner
author: Mayya Groza
author: Cindy Guichard
author: Gilles Lebeau
author: Roland Masson
published in: Numerische Mathematik
publication date: 2016-12-20T00:00:00Z
review text: The authors consider the anisotropic Darcy flow described by equations div~\(\mathbf q =h\) and \(\mathbf q=-\Lambda \nabla u\), where \(\Lambda\) is the permeability tensor. Equations in the weak formulation are stated. The conditions on the fractures \(\Gamma\) have the form div\(_{\tau} \mathbf q - [\mathbf q \cdot \mathbf n] =h_f\) and \(\mathbf q=-\Lambda_f \nabla_{\tau} \gamma u\), where div\(_{\tau}\) and \(\nabla_{\tau}\) denote the tangential operators on the surfaces \(\Gamma\). Here, \(\gamma\) is the trace operator, \(\mathbf n\) the unit normal vector to \(\Gamma\). Hence, the flow is considered in two manifolds with different dimensions. The gradient numerical scheme is applied to the hybrid dimensional flow model.
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 76M12
zbMATH DE Number: 6666243
zbMATH Keywords: weak formulation
reviewed by: Vladimir Mityushev
MaRDI profile type: Publication
full work available at URL: s00211-015-0782-x
OpenAlex ID: W171913366
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DOI: 10.1007/S00211-015-0782-X
description: scientific article; zbMATH DE number 6666243