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Y. Mohamady:
"robust exponential convergence of finite element methods for problems with boundary and interior layers";
Supervisor: J. Melenk; Institut für Analysis und Scientific Computing, 2021; final examination: 2021-09-15.

For a singularly perturbed model problem in 1D, robust exponential convergence of the hp-version of the finite element (hp-FEM) is shown. The solution features boundary layers as well as an interior layer due to nonsmoothness of the input data under consideration. To capture the boundary and the interior layer numerically, the mesh includes small elements of the size of the length scale of the layer to properly resolve them.