Adaptive discontinuous Galerkin methods on polytopic meshes

Collis, Joe and Houston, Paul (2016) Adaptive discontinuous Galerkin methods on polytopic meshes. In: X-DMS eXtended Discretization Methods, 9-11 Sept 2015, Ferrara, Italy.

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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.

Item Type: Conference or Workshop Item (Paper)
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 . Title of paper in conference programme: hp-Version Discontinuous Galerkin Methods on Polytopic Meshes
Keywords: discontinuous Galerkin methods; polytopic elements; hp–finite element methods
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
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Depositing User: Houston, Paul
Date Deposited: 01 Apr 2016 13:04
Last Modified: 04 May 2020 18:05

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