My main research interest is the numerical analysis of (nonlinear) partial differential equations in materials science and engineering, with a particular focus on liquid crystal theory, micromagnetism, and spintronics. I am also interested in fundamental questions in the analysis of finite element methods (a priori and a posteriori error estimates, convergence and optimality results for adaptive finite element schemes), uncertainty quantification (stochastic Galerkin methods for high-dimensional parametric elliptic problems), and adaptivity for model order reduction methods.