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A posteriori error estimation for discontinuous Galerkin methods on general meshes and adaptivity

Presented by: 
Andrea Cangiani
Date: 
Tuesday 22nd October 2019 - 09:55 to 10:40
Venue: 
INI Seminar Room 1
Abstract: 
The application and a priori error analysis of discontinuous Galerkin (dG) methods for general classes of PDEs under general mesh assumptions is by now well developed. dG methods naturally permits local mesh and order adaptivity. However, deriving robust error estimators allowing for curved/degenerating mesh interfaces as well as developing adaptive algorithms able to exploit such flexibility is non-trivial. In this talk we present recent work on a posteriori error estimates for dG methods of interior penalty type which hold on general mesh settings, including elements with degenerating and curved boundaries. The exploitation of general meshes within mesh adaptation algorithms applied to a few challenging problems will also be discussed.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons