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DTSTART;TZID=Europe/Paris:20260611T153000
DTEND;TZID=Europe/Paris:20260611T163000
DTSTAMP:20260407T090948
CREATED:20260203T195417Z
LAST-MODIFIED:20260305T191729Z
UID:14755-1781191800-1781195400@lmv.math.cnrs.fr
SUMMARY:EDP : Alexandre Ern (CERMICS\, ENPC) : Convergence of ERK-DG approximations of the first-order form of Maxwell's equations with low regularity
DESCRIPTION:We establish a convergence result for the approximation of low-regularity solutions to time-dependent PDE systems that have an involution structure similar to Maxwell’s equations and the linear wave equations.\nThe approximation is based on an explicit Runge–Kutta (ERK) time-stepping and the discontinuous Galerkin (dG) method with stabilization (so-called upwind fluxes) in space. The regularity setting only assumes that the exact solution and its first time-derivative are in L∞(0\,T;Hs(Ω)) with a Sobolev regularity index s in ]0\,1/2[ (here\, T is the time horizon and Ω the space domain)\, and that its second time-derivative is in L∞(0\,T;L2(Ω)).\nThe two main tools for the convergence analysis are a Ritz projection in space that leverages recent convergence results in operator norm for the dG approximation of the steady form of the PDE\, and the L2-stability under a standard CFL condition of three-stage\, third-order and four-stage\, fourth-order ERK schemes. These latter results are known in the literature\, but we provide here a somewhat simpler argumentation to prove the $L2$-stability. This is joint work with J.-L. Guermond (Texas A&M).
URL:https://lmv.math.cnrs.fr/evenenement/edp-alexandre-ern-cermics-enpc/
LOCATION:Bâtiment Fermat\, salle 4205
CATEGORIES:Séminaire EDP
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