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SUMMARY:Discontinuous Galerkin methods on arbitrarily shaped elements. - E
 mmanuil Georgoulis (University of Leicester\; National Technical Universit
 y of Athens)
DTSTART:20191022T101000Z
DTEND:20191022T105500Z
UID:TALK133096@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We extend the applicability of the popular interior-penalty di
 scontinuous Galerkin (dG) method discretizing advection-diffusion-reaction
  problems to meshes comprising extremely general\, essentially arbitrarily
 -shaped element shapes. In particular\, our analysis allows for curved ele
 ment shapes\, without the use of (iso-)parametric elemental maps. The feas
 ibility of the method relies on the definition of a suitable choice of the
  discontinuity-penal-ization parameter\, which turns out to be essentially
  independent on the particular element shape. A priori error bounds for th
 e resulting method are given under very mild structural assumptions restri
 cting the magnitude of the local curvature of element boundaries. Numerica
 l experiments are also presented\, indicating the practicality of the prop
 osed approach. Moreover\, we shall discuss a number of perspectives on the
  possible applications of the proposed framework in parabolic problems on 
 moving domains as well as on multiscale problems. The above is an overview
  of results from joint works with A. Cangiani (Nottingham\, UK)\, Z. Dong 
 (FORTH\, Greece / Cardiff UK) and T. Kappas (Leicester\, UK).<br><br><br><
 br><br>
LOCATION:Seminar Room 1\, Newton Institute
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