3 papers
math.NA2020
Coupled Flow and Mechanics in a 3D Porous Media with Line Sources
Nadia S. Taki, Ingeborg G. Gjerde
In this paper, we consider the numerical approximation of the quasi-static, linear Biot model in a 3D domain when the right-hand side of the mass balance equation is concentrat…
math.AP2019
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…
math.NA2018
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…