Speaker
Paul Houston, University of Nottingham
Abstract
In recent years there has been considerable interest in the design of numerical methods that support computational meshes composed of general polygonal and polyhedral (polytopic, for short) elements. Indeed, such approaches naturally allow for the treatment of complex geometries in an efficient manner and moreover they can easily be exploited in the design of multi-level solvers, such as multigrid and Schwarz-type preconditioners, for example.
In this talk we present a brief overview of the application of high-order/hp-version discontinuous Galerkin finite element methods (DGFEMs) posed on general polytopic meshes. Here, we discuss both the theoretical and practical challenges of exploiting DGFEMs within such a general setting, with particular application to the numerical approximation of the linear Boltzmann transport problem. We study both the stability and a priori error analysis of the proposed scheme, as well as outlining its implementation based on exploiting fast numerical integration techniques. Numerical experiments are presented to highlight the practical performance of the proposed method.