Approximation of Viscosity Solutions for Nonlinear PDEs

Construction and analysis of approximation schemes for Hamilton­-Jacobi type equations of first and second order on Euclidean spaces, networks and stratified domains. 

Homogenization and approximation of effective hamiltonians. Finite difference, Finite volumes and semi-Lagrangian schemes on structured/unstructured grids: accuracy, stability and convergence. A priori and a posteriori error estimates. Numerical treatement of Boundary Conditions. Adaptive methods. High­ order accurate approximation schemes. Acceleration methods: fast marching, fast sweeping, fast iterative, domain decomposition, point location via Quadtree/Octree search and Walking search. CUDA implementations on GPUs.

 Numerical methods for Mean Curvature Motion, game p-laplacian equation, levet set methods and related models in image processing.

Components: Simone Cacace and Elisabetta Carlini