Exploiting Superconvergence in Discontinuous Galerkin Methods for Improved Time-Stepping and Visualization
Technical Report,01 Feb 2013,31 Jul 2016
UNIVERSITY OF EAST ANGLIA, School of Mathematics NORWICH United Kingdom
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The discontinuous Galerkin DG method continues to maintain heightened levels of interest within the simulation community because of the discretization flexibility it provides. Although one of the fundamental properties of the DG methodology and arguably its most powerful property is the ability to combine high order discretizations on an inter-element level while allowing discontinuities between elements, this flexibility generates a plethora of difficulties. First, by evolving more degrees of freedom, a more restrictive CFL condition is needed, which is computationally expensive. Secondly, the lack of continuity across element interfaces hampers visualization efforts as many visualization packages assume higher levels of continuity. However, DG also has the property of superconvergence. That is, it achieves essentially twice the usual convergence rate at specific points within the mesh, or in a special norm, allowing for faster convergence to a reasonable solution. The goal of this research is to exploit the inherent property of superconvergence in order to1 create a better pairing between DG solutions and the time-stepping method used, and 2 create filters that allow highly accurate visualization of DG data.
- Operations Research
- Computer Programming and Software