222 citations · 937 across the 65 of their papers we have counts for
11 papers · 1 filter
On the optimization of the fixed-stress splitting for Biot's equations
Erlend Storvik, Jakub Wiktor Both, Kundan Kumar +2
In this work we are interested in effectively solving the quasi-static, linear Biot model for poromechanics. We consider the fixed-stress splitting scheme, which is a popular metho…
A Singularity Removal Method for Coupled 1D-3D Flow Models
Ingeborg G. Gjerde, Kundan Kumar, Jan M. Nordbotten
In reservoir simulations, the radius of a well is inevitably going to be small compared to the horizontal length scale of the reservoir. For this reason, wells are typically modell…
A multipoint stress mixed finite element method for elasticity on quadrilateral grids
Ilona Ambartsumyan, Eldar Khattatov, Jan M. Nordbotten +1
We develop a multipoint stress mixed finite element method for linear elasticity with weak stress symmetry on quadrilateral grids, which can be reduced to a symmetric and positive…
Splitting method for elliptic equations with line sources
Ingeborg G. Gjerde, Kundan Kumar, Jan M. Nordbotten +1
In this paper, we study the mathematical structure and numerical approximation of elliptic problems posed in a (3D) domain when the right-hand side is a (1D) line source . T…
Guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the Biot problem
Kundan Kumar, Svetlana Kyas, Jan Nordbotten +1
The paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi-static linear Biot equat…
Well-posedness of the fully coupled quasi-static thermo-poro-elastic equations with nonlinear convective transport
Mats K. Brun, Elyes Ahmed, Florin A. Radu +1
This paper is concerned with the analysis of the quasi-static thermo-poroelastic model. This model is nonlinear and includes thermal effects compared to the classical quasi-static…
Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media
Jakub Wiktor Both, Kundan Kumar, Jan Martin Nordbotten +1
In this paper, we study the robust linearization of nonlinear poromechanics of unsaturated materials. The model of interest couples the Richards equation with linear elasticity equ…
A multipoint stress mixed finite element method for elasticity on simplicial grids
Ilona Ambartsumyan, Eldar Khattatov, Jan M. Nordbotten +1
We develop a new multipoint stress mixed finite element method for linear elasticity with weakly enforced stress symmetry on simplicial grids. Motivated by the multipoint flux mixe…
A Non-standard Model for Microbial Enhanced Oil Recovery Including the Oil-water Interfacial Area
David Landa-Marbán, Florin A. Radu, Jan M. Nordbotten
In this work we present a non-standard model for microbial enhanced oil recovery including the oil-water interfacial area. Including the interfacial area in the model, we eliminate…
Unified approach to discretization of flow in fractured porous media
Jan M. Nordbotten, Wietse M. Boon, Alessio Fumagalli +1
In this paper, we introduce a mortar-based approach to discretizing flow in fractured porous media, which we term the mixed-dimensional flux coupling scheme. Our formulation is agn…
Linear iterative schemes for doubly degenerate parabolic equations
Jakub W. Both, Kundan Kumar, Jan M. Nordbotten +2
Mathematical models for flow and reactive transport in porous media often involve non-linear, degenerate parabolic equations. Their solutions have low regularity, and therefore low…