Oberseminar Numerische Mathematik / Scientific Computing
Alexandre Ern
Ecole des Ponts Paris Tech
Discrete functional analysis tools for Discontinuous Galerkin methods
Abstract:
Two discrete functional analysis tools are established for spaces of piecewise polynomial functions on general meshes: (i) a discrete counterpart of the continuous Sobolev embeddings, in both Hilbertian and non-Hilbertian settings; (ii) a compactness result for bounded sequences in a suitable Discontinuous Galerkin norm, together with a weak convergence property for some discrete gradients. The proofs rely on techniques inspired by the Finite Volume literature, which differ from those commonly used in Finite Element analysis. The discrete functional analysis tools are used to prove the convergence of Discontinuous Galerkin approximations of the steady incompressible Navier--Stokes equations.
| Datum: | 18.05.09 | Zeit: | 14:15 Uhr | Ort: | Zuse Institut Berlin, Takustr. 7, 14195 Berlin. | Raum: | Seminarraum im Erdgeschoss |