Skip to main content

Research Repository

Advanced Search

Adaptive discontinuous Galerkin methods on polytopic meshes

Collis, Joe; Houston, Paul

Authors

Joe Collis Joe.Collis@nottingham.ac.uk

PAUL HOUSTON paul.houston@nottingham.ac.uk
Professor of Computational and Applied Maths



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Peer Reviewed Not Peer Reviewed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 http://eprints.nottingham.ac.uk/id/eprint/32578
Publisher URL http://link.springer.com/chapter/10.1007%2F978-3-319-41246-7_9
Related Public URLs http://x-dms2015.sciencesconf.org/
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf
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