In this paper, we study the mathematical structure and numerical approximation of elliptic
problems posed in a (3D) domain Ω when the right-hand side is a (1D) line source Λ. The …

Flow in vascularized biological tissue, root water uptake, or flow around injection or
extraction wells can be modeled by coupled mixed-dimensional PDE systems …

We are interested in a convergent numerical discretization scheme for nonlinear differential
algebraic equations (DAEs) coupled with elliptic constraints. The dynamics of flow networks …

A model of groundwater flow in porous media influenced by wells (boreholes, channels) is
considered. The model is motivated by the reduced dimension approach which suits …

In this work, a numerical solution technique for an elliptic Dirac problem is investigated. One
reason to study this issue is that this partial differential equation (PDE) is closely related to a …

Coupled systems of differential-algebraic equations (DAEs) and partial differential equations
(PDEs) appear in various fields of applications such as electrical engineering, bio …

In the previous chapters we have discussed a mathematical model for simulating blood flow
and transport processes in large arteries. Since the model contains non-linear terms and …

The introductory chapter of the submitted thesis is divided into three parts: In the first part we
describe four flow processes from different application areas which are examined in the …

In this thesis, we consider a specific instance of mixed-dimensional partial differential
equations (PDEs) commonly referred to as the coupled 1D-3D flow model. The model itself …

In this doctoral thesis, a model of groundwater flow in porous media influenced by wells
(boreholes, channels) is developed. The model is motivated by the reduced dimension …