In this talk we’ll present arbitrary-order hybrid discretizations of Friedrichs systems. Friedrichs systems provide a framework that goes beyond the standard classification of partial differential equations into hyperbolic or elliptic, and are thus particularly suited for problems that include both diffusive and advective terms. After presenting a gallery of problems that can be recast in Friedrichs’ formalism, we present a family of numerical schemes hinging on hybrid spaces with unknowns located at elements and faces. Hybrid schemes support general meshes, are locally conservative and, compared with traditional Discontinuous Galerkin discretizations, lead to smaller algebraic systems once static condensation has been applied. We carry out a complete stability and convergence analysis, which appears to be the first of its kind. The performance of the method is illustrated on scalar and vector three-dimensional diffusion-advection-reaction problems.

Contatto:
paola.antonietti@polimi.it