High Order Schemes for Conservation lawsÂ
High Order Schemes for Conservation lawsÂ
Many phenomena in science are described by means of systems of nonlinear hyperbolic balance laws. They include gas dynamics, shallow water flows, plasmas. These equations are usually not solvable analytically. It is thus necessary to design robust numerical schemes to compute their approximate solutions. We work on the development and study of efficient and high-order accurate finite volume, finite element and discontinuous Galerkin methods for the numerical evolution of hyperbolic PDEs, such as CWENO schemes and their implicit formulation (Quinpi), ADER-DG schemes and Deferred Correction schemes, and high order schemes based on Lagrange Galerkin methods for Fokker Plank equations.
Components: Elisabetta Carlini, Gabriella Puppo, Davide Torlo and Giuseppe Visconti
Recent works
M. Briani, G. Puppo, G. Visconti. Dissipation-dispersion analysis of fully-discrete implicit discontinuous Galerkin methods and application to stiff hyperbolic problems. Submitted. 2024. (Preprint: arXiv:2410.05901)
G. Puppo, M. Semplice, G. Visconti. Quinpi: Integrating stiff hyperbolic systems with implicit high order finite volume schemes. Commun. Comput. Phys., 36(1):30-70. 2024.
G. Puppo, M. Semplice, G. Visconti. Quinpi: integrating conservation laws with CWENO implicit methods. Commun. Appl. Math. Comput., 5:343-369. 2023.