Research
My research interests combine the development and analysis of mathematical models and of the ensuing numerical methods for the simulation of natural phenomena. I consider my work to be at the interface between applied mathematics and applications, and my personal aspirations is to contribute with my expertise to the solution of problems with social and environmental impacts.
Research Interests
Scalar-, Vector- and Tensor-valued surface PDEs: development of numerical methods adapted to the geometry for PDEs on surfaces (intrinsic finite volumes, Discontinuous Galerkin, surface finite element, high-order virtual element methods). Applications to surface fluid flows, including shallow water equations and two-phase flow with curvature effects on stationary and evolving surfaces.
Intrinsic Shallow Water Equations (ISWE) on fixed and moving surfaces: modeling and development of numerical methods to solve ISWE (finite volumes with Eulerian and Lagrangian-Eulerian approach, discontinuous Galerkin scheme, continuous Galerkin with entropy-viscosity stabilization).
Coupling of 1D, 2D and 3D models: formulation and numerical solution of geometrically intrinsic models of two-dimensional overland flows for coupled surface-subsurface hydrological applications; numerical modeling of flow and transport equations in porous media with strong anisotropy; development of unfitted methods for embedded low-dimensional features.