Research
My research interests combine the study of mathematical models and the development of suitable numerical methods with applications to different physical phenomena. My personal aspirations is to contribute with my expertise to the solution of problems with social and environmental impacts.
Research Interests
Development of numerical methods adapted to the geometry for PDEs on surfaces: intrinsic surface finite elements methods, high-order virtual elements method.
Modeling of Intrinsic Shallow Water Equations (ISWE) on fixed and moving surfaces 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).
Numerical modeling of flow and transport equations in porous media (two and three dimensional cases): study of strong anisotropic cases, coupling of surface and subsurface processes.
Vector- and Tensor-valued surface PDEs: numerical methods for surface fluids, numerical modeling of two-phase flow including curvature effects on stationary and evolving surfaces.