Karl Erik Holter successfully defended his PhD

Main research findings

In the natural sciences, there are many examples of physical systems which can be modelled by differential equations, such as the flow of water through soil or the deformation of a bridge under load. By developing mathematical techniques for solving the resulting equations with a computer, we can use these models to answer questions such as how much weight a bridge can support before collapsing.

Complex systems often involve multiple interdependent kinds of physical behaviour. An example is the brain, where water movement occurs both inside blood vessels and in the surrounding brain tissue. Because the two kinds of flow affect each other through interchange across the vessel walls, a model of water movement in the brain must account for both.

However, even when there are robust methods for solving either subproblem individually, coupling them together in a robust manner is not always straightforward, and the focus of this thesis. Robustness means that the method should run in a reasonable amount of time, both for complex problems with many unknowns and for all values of the problem parameters, even the very large or very small. This property is crucial for applications such as water movement in the brain.

The work has been conducted at Simula Research Laboratory and UiO.

Prior to the defence, Karl Erik Holter presented his trial lecture «Finite element approximation of eigenvalue problems».

The PhD defence and trial lecture were fully digital.

Adjudication committee:

• Professor Lucia Gastaldi, University of Brescia, Italy
• Associate Professor Mingchao Cai, Morgan State University, USA
• Professor Snorre Christiansen, Department of Mathematics, University of Oslo, Norway

Supervisors

• Professor Kent-Andre Mardal, Department of Mathematics, University of Oslo, Norway
• Professor Anders M. Dale, University of California, San Diego
• Associate Professor Unn Kristin H. Haukvik, Faculty of Medicine, Institute of Clinical Medicine, University of Oslo, Norway

​Chair of defence

• Professor & Head of Department Stephan Oepen, Department of Informatics, UiO