Three new papers

The following three papers have recently been published:

  1. A paper on robust solvers for phase-field models in CMAME by Mats Brun et al. The presented solver seems to significantly reduce the number of iterations comparing with existing approaches.


  1. The recent paper ‘Rigourous upscaling of unsaturated flow in fractured porous media´ concerns upscaled models for domains containing a fracture. Both the matrix and fracture are assumed to be unsaturated. Effective models are rigorously derived. The paper appeared in SIAM Journal of Mathematical Analysis and was written by Florian List, Kundan Kumar, Iuliu Pop, and Florin Radu.


  1. A paper on upscaling of permeable biofilm in different geometries in Transport in Porous Media: An Upscaled Model for Permeable Biofilm in a Thin Channel and Tube by David Landa-Marban et al.

Multi-Point approximations for thermo-poroelasticity

Jan and Eirik have just uploaded a new paper entitled An introduction to Multi-Point Flux (MPFA) and Multi-Point Stress (MPSA) Finite Volume Methods for Thermo-Poroelasticity, to arxiv. The paper gives a unified presentation of the MPFA/MPSA family of methods, including formulation, method properties and implementational aspects. The paper covers much of the development that has taken place since Ivar Aavatsmark wrote his introduction to MPFA almost 20 years ago.

Higher order FE schemes for the wave equation

A paper has recently appeared in Mathematics of Computations:

Post-processed Galerkin approximation of improved order for wave equations by M. Bause, U. Koecher, F.A. Radu and F. Schieweck,

The paper is about higher order FE schemes in time and space for the wave equation. The main point is the introduction of a post processing to increase the order of convergence in time. Rigorous analysis and numerical experiments are presented.

Flow upscaling in fractured porous media

A paper has recently appeared in Journal of Computational Physics:

Formal upscaling and numerical validation of unsaturated flow models in fractured porous media by F.List, K. Kumar, I.S. Pop and F.A. Radu

Formal upscaling is performed for a domain containing one fracture. The medium is assumed to be unsaturated. Depending on the ratio between the permeability/porosity in the fracture and in the outer medium a cascade of models is obtained. The paper aims to answer which is the right model to be used in the different cases.

Visit from Heidelberg

The group has the honour of hosting Dr. Markus Ghan from the University of Heidelberg in the period 06-11.01.2020. Dr. Ghan is an expert in upscaling, homogenisation and applications to life science problems.

Visiting Stuttgart

As reported in a previous post, Professor Rainer Helmig joined the PMG in the Magne Espedal honorary position. During Helmig’s visit to Bergen in April, I was invited to visit the Institute for Modelling Hydraulic and Environmental Systems in Stuttgart for two months this fall. The purpose of the stay was to meet, discuss and collaborate with members of the group working on similar problems as myself, i.e. coupled thermo-poroelasticity and fracture deformation. In addition to the inspiring scientific discussions, it was a true pleasure to get to know the members of the group!

During my visit, I was briefly joined by another PMG member. Inga Berre managed to squeeze in both a presentation at the group’s seminar and an interview with Carina Bringedal, who happens to be a former member of the group now employed at the University of Stuttgart.

David Landa-Marbán's PhD defence

Congratulations to David Landa-Marbán with his successful PhD defence on June 14! Here is a summary of the thesis, which has the title Mathematical modeling of microbial enhanced oil recovery with focus on bio-plug technology: from the pore to the core scale.

Mats Kirkesæther Brun's PhD defence

We warmly congratulate Mats Kirkesæther Brun on his successful PhD defence today. A brief description of the thesis, Upscaling, analysis and iterative numerical solution schemes for thermo-poroelasticity, can be found here.



We are very satisfied with the group’s strong presence at the SIAM GS 2019. Through our numerous (excellent!) presentations, participation as organisers of minisymposia and sheer number of participants, we definitely made our mark on the conference. Also, Inga Berre was elected as a SIAM GS officer and secretary of the SIAG Geosciences committee.

SIAM GS - Part I

Some fifteen members of the PMG are going to the SIAM GS 2019 conference. We take part as organisers of the following minisymposia:

Verification Benchmarks for Single-phase Flow in Three-dimensional Fractured Porous Media: Inga Berre, Eirik Keilegavlen and Ivar Stefansson

Advances in Modeling of Non-linear Elasticity and Plasticity for Geomaterials: Inga Berre and Michele Starnoni

Also, we highly recommend attending the following talks:


9.45 Local and Semi-local Modeling and Discretization Principles for Fractured Porous Media by Jan M Nordbotten

11.00 Block Preconditioners for Mixed-dimensional Flow Problems in Fractured Porous Media by Ana Budisa

2.40 Numerical Modeling of Fracture Reactivation in a Three-dimensional Domain Based on a Coulomb Friction Law by Runar Lie Berge

3.05 The Mathematical Structure of Coupled 1D-3D Models by Ingeborg G Gjerde

4.50 Iterative Solvers for Poromechanics with Large Deformation by Manuel Borregales

5.30 A Pore-scale Study of the Transport of Inertial Particles in Porous Media by Max Endo Kokubun


2.15 Challenges in Modelling the Anisotropic Poroelastoplastic Behaviour of Fractured Rocks as Homogenized Media by Michele Starnoni


3.55 Mathematical Modelling of the Bio-plug Technology: Laboratory Experiments, Upscaling, and Numerical Simulations by David Landa Marban

5.50 Monolithic and Splitting Based Solution Schemes for Nonlinear Quasi-static Thermo-poroelasticity by Mats Kirksæther Brun

6.30 Gradient Flow Perspective on Poromechanics by Jakub Both


10.10 Numerical Methods for Flow in Fractured Porous Media in a Unified Implementation by Ivar Stefansson

11.00 Mixed-dimensional Discrete Fracture Matrix Models with Heterogeneous Discretizations and Non-matching Grids by Eirik Keilegavlen


An update will follow once the delegation is back from Houston!