Presented by:
Emmanuil Georgoulis
Date:
Tuesday 22nd October 2019 - 11:10 to 11:55
Venue:
INI Seminar Room 1
Event:
Abstract:
We
extend the applicability of the popular interior-penalty discontinuous 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 element shapes, without the use of
(iso-)parametric elemental maps. The feasibility 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 the resulting method are given under very mild
structural assumptions restricting the magnitude of the local curvature of
element boundaries. Numerical experiments are also presented, indicating the
practicality of the proposed 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).