222 citations · 937 across the 65 of their papers we have counts for
12 papers · 1 filter
The fixed-stress splitting scheme for Biot's equations as a modified Richardson iteration: Implications for optimal convergence
Erlend Storvik, Jakub Wiktor Both, Jan Martin Nordbotten +1
The fixed-stress splitting scheme is a popular method for iteratively solving the Biot equations. The method successively solves the flow and mechanic subproblems while adding a st…
A Mixed Approach to the Poisson Problem with Line Sources
Ingeborg G. Gjerde, Kundan Kumar, Jan M. Nordbotten
In this work we consider the primal mixed variational formulation of the Poisson equation with a line source. The analysis and approximation of this problem is non-standard as the…
The gradient flow structures of thermo-poro-visco-elastic processes in porous media
Jakub Wiktor Both, Kundan Kumar, Jan Martin Nordbotten +1
In this paper, the inherent gradient flow structures of thermo-poro-visco-elastic processes in porous media are examined for the first time. In the first part, a modelling framewor…
Numerical simulations of viscous fingering in fractured porous media
Runar Lie Berge, Inga Berre, Eirik Keilegavlen +1
The effect of heterogeneities induced by highly permeable fracture networks on viscous miscible fingering in porous media is examined using high-resolution numerical simulations. W…
Robust linear domain decomposition schemes for reduced non-linear fracture flow models
Elyes Ahmed, Alessio Fumagalli, Ana Budiša +3
In this work, we consider compressible single-phase flow problems in a porous media containing a fracture. In the latter, a non-linear pressure-velocity relation is prescribed. Usi…
Iterative solvers for Biot model under small and large deformation
Manuel Antonio Borregales, Kundan Kumar, Jan Martin Nordbotten +1
We consider L-scheme and Newton based solvers for Biot model under small or large deformation. The mechanical deformation follows the Saint Venant-Kirchoff constitutive law. Furthe…
A combined finite element-finite volume framework for phase-field fracture
Juan Michael Sargado, Eirik Keilegavlen, Inga Berre +1
Numerical simulations of brittle fracture using phase-field approaches often employ a discrete approximation framework that applies the same order of interpolation for the displace…
Finite volume discretization for poroelastic media with fractures modeled by contact mechanics
Runar L. Berge, Inga Berre, Eirik Keilegavlen +2
A fractured poroelastic body is considered where the opening of the fractures is governed by a nonpenetration law while slip is described by a Coulomb-type friction law. This physi…
An iterative staggered scheme for phase field brittle fracture propagation with stabilizing parameters
Mats Kirkesæther Brun, Thomas Wick, Inga Berre +2
This paper concerns the analysis and implementation of a novel iterative staggered scheme for quasi-static brittle fracture propagation models, where the fracture evolution is trac…
Stable Mixed Finite Elements for Linear Elasticity with Thin Inclusions
Wietse M. Boon, Jan M. Nordbotten
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions an…
Monolithic and splitting based solution schemes for fully coupled quasi-static thermo-poroelasticity with nonlinear convective transport
Mats Kirkesæther Brun, Elyes Ahmed, Inga Berre +2
This paper concerns splitting-based iterative procedures for the coupled nonlinear thermo-poroelasticity model problem. The thermo-poroelastic model problem we consider is formulat…
Adaptive asynchronous time-stepping, stopping criteria, and a posteriori error estimates for fixed-stress iterative schemes for coupled poromechanics problems
Elyes Ahmed, Jan Martin Nordbotten, Florin Adrian Radu
In this paper we develop adaptive iterative coupling schemes for the Biot system modeling coupled poromechanics problems. We particularly consider the space-time formulation of the…