In this thesis we consider model reduction for parameter dependent parabolic PDEs defined on
networks with variable composition. For this type of problem the Reduced Basis Element Method
(RBEM) developed by Maday and Rønquist is a reasonable choice as a solution on the entire
domain is not required. The reduction method is based on the idea of constructing a reduced
basis for every individual component and coupling the reduced elements using a mortar-like
method. However this decomposition procedure can lead to difficulties especially for networks
consisting of numerous edges. Due to the variable composition of the networks the solution on
the interfaces is extremely difficult to predict. This can lead to unsuitable basis functions
and poor approximations of the global solutions. On the basis of networks consisting of
one-dimensional domains we present an extension of the RBEM which remedies this problem and
provides a good basis representation for each individual edge. Essentially this extension makes
use of a splinebased boundary parametrization in the local basis construction. To substantiate
the approximation properties of the basis representation onto the global solution we develop
an error estimate for local basis construction with Proper Orthogonal Decomposition (POD) or
POD-Greedy. Additionally we provide existence uniqueness and regularity results for parabolic
PDEs on networks with one-dimensional domains which are essential for the error analysis.
Finally we illustrate our method with three examples. The first corresponds to the theory
presented and shows two different networks of one-dimensional heat equations with varying
thermal conductivity. The second and third problem demonstrates the extensibility of the method
to component based domains in two dimensions or nonlinear PDEs. These were parts of the
research project Life-cycle oriented optimization for a resource and energy efficient
infrastructure funded by the German Federal Ministry of Education and Research.
