Adaptive discontinuous Galerkin methods on polytopic meshes

Collis, Joe; Houston, Paul

Abstract

In this article we consider the application of discontinuous Galerkin finite element methods, defined on agglomerated meshes consisting of general polytopic elements, to the numerical approximation of partial differential equation problems posed on complicated geometries. Here, we assume that the underlying computational domain may be accurately represented by a geometry-conforming fine mesh; the resulting coarse mesh is then constructed based on employing standard graph partitioning algorithms. To improve the accuracy of the computed numerical approximation, we consider the development of goal-oriented adaptation techniques within an automatic mesh refinement strategy. In this setting, elements marked for refinement are subdivided by locally constructing finer agglomerates; should further resolution of the underlying fine mesh T_f be required, then adaptive refinement of T_f will also be undertaken. As an example of the application of these techniques, we consider the numerical approximation of the linear elasticity equations for a homogeneous isotropic material. In particular, the performance of the proposed adaptive refinement algorithm is studied for the computation of the (scaled) effective Young's modulus of a section of trabecular bone.

Citation

Collis, J., & Houston, P. (2016). Adaptive discontinuous Galerkin methods on polytopic meshes.

• Conference Name: X-DMS eXtended Discretization Methods
• End Date: Sep 11, 2015
• Acceptance Date: Apr 30, 2015
• Publication Date: Aug 25, 2016
• Deposit Date: Apr 1, 2016
• Peer Reviewed: Not Peer Reviewed
• Keywords: discontinuous Galerkin methods; polytopic elements; hp–finite element methods
• Public URL: https://nottingham-repository.worktribe.com/output/804449
• Publisher URL: http://link.springer.com/chapter/10.1007%2F978-3-319-41246-7_9
• Related Public URLs: http://x-dms2015.sciencesconf.org/
• Additional Information: Published in: Advances in discretization methods: discontinuities, virtual elements, fictitious domain methods. Cham : Springer, 2016. ISBN 978-3-319-41246-7. pp. 187-206, doi: 10.1007/978-3-319-41246-7_9 http://link.springer.com/chapter/10.1007%2F978-3-319-41246-7_9 . Title of paper in conference programme: hp-Version Discontinuous Galerkin Methods on Polytopic Meshes