Numerical analysis of partial differential equations (PDEs). in particular:
- Computational (nonlinear) PDEs in materials science and engineering: liquid crystals; micromagnetics; spintronics.
- Finite element method (FEM) and boundary element method (BEM): a priori and a posteriori error analysis; convergence and optimality of adaptive algorithms.
- Uncertainty quantification and model order reduction: (goal-oriented) adaptivity for stochastic Galerkin FEM and model order reduction methods.
