Ceren Gurkan obtained her bachelor’s degree in Civil Engineering from Middle East Technical University (Ankara/Turkey) in 2011. She then participated in the Erasmus Mundus in Computational Mechanics program and received her MSc degree from Universitat Politecnica de Catalunya and Swansea University in 2013. She is currently a PhD candidate under the Erasmus Mundus Simulation in Engineering and Entrepreneurship Development (SEED) program at Universitat Politecnica de Catalunya and Technical University of Munich, under the supervision of Assoc.Prof. Sonia Fernandez Mendez and Dr. Martin Kronbichler.

This thesis proposes a new numerical technique: the eXtended Hybridizable Discontinuous Galerkin (X-HDG) Method, to efficiently solve problems including boundaries and interfaces. It aims to outperform available methods and improve the results by inheriting favored properties of Hybridizable Discontinuous Galerkin (HDG) together with an explicit interface definition. X-HDG combines the Hybridizable Discontinuous Galerkin method with an eXtended Finite Element (X-FEM) philosophy, with a level set description of the interface, to form an hp convergent, high order unfitted numerical method. HDG outperforms other Discontinuous Galerkin (DG) methods for problems involving self-adjoint operators, due to its hybridization and superconvergence properties. The hybridization process drastically reduces the number of degrees of freedom in the discrete problem, similarly to static condensation in the context of high-order Continuous Galerkin (CG). This work demonstrates that X-HDG keeps the optimal and superconvergence of HDG with no need of mesh fitting to the interface.