The group focuses on methods for the numerical treatment of partial differential equations (PDEs) emerging in engineering and physics applications, such as electromagnetism, thermal insulation, solid mechanics, or material science, or in image processing problems in application fields such as astronomy, biomedicine, and archaeology. The group's research includes the design and the theoretical analysis of numerical schemes, numerical validation of the results obtained, and the application of the developed methods in the simulation of relevant problems in applications.
The following is a (non-exhaustive) list of research topics of interest:
- Finite element method for (systems of) (nonlinear) PDEs arising in multiphysics problems
- A posteriori error estimates and adaptivity for finite elements
- Acceleration and structured techniques for linear systems stemming from PDE discretizations
- Stochastic Galerkin methods for high-dimensional parametric PDEs from uncertainty quantification problems
- Numerical methods for Hamilton-Jacobi equations arising in image processing or 3D printing problems
- Development of semi-Lagrangian schemes for nonlinear PDEs, and related convergence analysis
- Development of adaptive high-order numerical methods and related stability and convergence study for evolutionary problems, mostly in the area of fronts propagation with Level-Set approach and its variants.