Short Course "Solvers for nonlinear and/or coupled problems in porous media"

This short course took place at the University of Stuttgart from February 2 to 8, 2019.

General Information

February 2 - 8, 2019

University of Stuttgart, Pfaffenwaldring 57, room 2.136

Members and associated international members of SFB 1313 and IRTG DROPIT are invited to attend the short course. Participants will get 3 credits for attending the course.

Requirements: linear algebra, finite element or finite volume method, a laptop
and a software package for solving PDEs (like DUNE, Fenics or even Matlab).

The course is free of charge. Possible costs for accommodation or travel expenses cannot be reimbursed.

The aim of this compact course is to give an overview over the most important techniques for solving nonlinear and/or coupled problems in porous media. Two model problems will be considered: the Richards equation and the (saturated
and unsaturated) Biot equations. Linearization techniques, i.e. Newton method, L-scheme and Picard method will be presented. The convergence of the resulting schemes will be discussed. The techniques will be applied to Richards ́ equation and implemented (FE or FV can be used). A study on the advantages and disadvantages of these methods w.r.t. efficiency and robustness will be performed (see [1]).

In the second part of the course iterative schemes, e.g. the fixed-stress method for the fully coupled Biot equations will be presented and implemented (see [2]). Nonlinear extensions (incl. unsaturated poromechanics) of the model and
application of iterative schemes in combination with linearization will be then discussed (se [3, 4]).

1. F. List, F.A. Radu, A study on iterative methods for Richards ́ equation, Computational Geosciences 20, 2016, pp. 341-353.
2. J. W. Both, M. Borregales, J.M. Nordbotten, K. Kumar, F.A. Radu, Robust fixed stress splitting for Biot ́s equation in heterogeneous media, Applied Math. Letters 68, 2017, pp. 101-108.
3. M. Borregales, F.A. Radu, K. Kumar, J.M. Nordbotten, Robust schemes for non-linear poromechanics, Computational Geosciences 22, 2018, pp. 1021-1038.
4. J. W. Both, K. Kumar, J.M. Nordbotten, F.A. Radu, Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media, Computers and Mathematics with Applications, 2018, DOI:


This course is given by Prof. Florin Adrian Radu, Manuel Antonio Borregales Reverón and Erlend Storvik from the Department of Mathematics, University of Bergen (Norway).

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