Doctor's Theses (authored and supervised):
"Finite element analysis of the heterogeneous Helmholtz equation and least squares methods";
Supervisor, Reviewer: J. Melenk, S. Nicaise, S. Sauter;
Institut für Analysis und Scientific Computing,
oral examination: 2021-07-22.
The present thesis is concerned with three main topics. The first on beeing at least squares finite element approach for numerical discretizations of the homogeneous Helmholtz equation. We perform a wave number-explicit convergence theory for this method. Secondly, we prove optimality for a first order system least squares finite element methodd applied to second order partial differential equations focusing on minimal regularity assumptions on the data. Finally, we consider a class of time-harmonic wave propagation problems in piecewise smooth media. For these problems, a wavenumber-explicit regularity theory is performed. This in turn allows for a complete and wavenumber-explicit convergence analysis of a Galerkin method applied to our model class.
Helmholtz equation; hp-version of finite element method; least squares method
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
Created from the Publication Database of the Vienna University of Technology.