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- Numerical Methods for Partial Differential Equations
- Polygonal and polyhedral methods (Discontinuous Galerkin, Virtual Element and Mimetic Finite Difference methods)
- Domain Decomposition and Multigrid Methods
- Seismic wave propagation problems (Project SPEED: SPectral Elements in Elastodynamics with Discontinuous Galerkin)
- Mathematical and numerical modeling of neurodegenerative disorders
- Flows in fractured porous media
- Mathematical and numerical modeling of polymer manufacturing technology