BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//wp-events-plugin.com//7.2.3.1//EN
TZID:Europe/Paris
X-WR-TIMEZONE:Europe/Paris
BEGIN:VEVENT
UID:1701@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20170411T110000
DTEND;TZID=Europe/Paris:20170411T120000
DTSTAMP:20170327T090000Z
URL:https://www.i2m.univ-amu.fr/evenements/discontinuous-galerkin-finite-e
 lement-approximation-of-hamilton-jacobi-bellman-equations-with-cordes-coef
 ficients/
SUMMARY: (...):  Discontinuous Galerkin finite element approximation of Ham
 ilton–Jacobi–Bellman equations with Cordes coefficients
DESCRIPTION:: Elliptic and parabolic Hamilton—Jacobi—Bellman equations 
 are an important class of second-order fully nonlinear PDEs\, with applica
 tions to stochastic optimal control problems in engineering and finance. I
 t is known that existing finite difference and finite element methods base
 d on discrete maximum principles can often be guaranteed to converge to th
 e viscosity solution in the small mesh limit. However\, the requirement fo
 r a discrete maximum principle imposes severe restrictions on the choice o
 f mesh\, the order of convergence and the size of the stencil for strongly
  anisotropic problems\, which can limit the computational efficiency on pr
 actical mesh sizes. This motivates the search for more flexible high-order
  methods that achieve the key properties of consistency\, stability and co
 nvergence without discrete maximum principles. In this talk\, we will pres
 ent how these challenges are overcome in the context of fully nonlinear se
 cond-order elliptic and parabolic Hamilton–Jacobi–Bellman equations th
 at satisfy a structural property named the Cordes condition. We construct 
 an hp-version discontinuous Galerkin finite element method which is motiva
 ted by the PDE theory of the problem. Both the continuous and discrete ana
 lyses are based on a variational strong monotonicity argument which establ
 ishes well-posedness of the fully nonlinear HJB PDE in the class of strong
  solutions\, and of the discrete numerical scheme. We show that the numeri
 cal method is consistent and stable\, with error bounds that are optimal i
 n the mesh size\, and suboptimal in the polynomial degrees\, as standard f
 or hp-version DGFEM. For parabolic problems\, the discretisation is extend
 ed by a high-order DG time-stepping method\, permitting high-order approxi
 mation in both time and space. Numerical experiments demonstrate the accur
 acy and efficiency of the numerical scheme on problems featuring strongly 
 anisotropic diffusion coefficients and singular solutions\, including expo
 nential convergence rates under hp-refinement. This is a joint work with P
 rof. Endre Süli\, University of Oxford.https://who.rocq.inria.fr/Iain.Sme
 ars/
CATEGORIES:Séminaire,Analyse Appliquée
END:VEVENT
BEGIN:VTIMEZONE
TZID:Europe/Paris
X-LIC-LOCATION:Europe/Paris
BEGIN:DAYLIGHT
DTSTART:20170326T030000
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
END:DAYLIGHT
END:VTIMEZONE
END:VCALENDAR