Goal-oriented adaptive composite discontinuous Galerkin methods for incompressible flows

Giani, Stefano; Houston, Paul

Abstract

In this article we consider the application of goal-oriented mesh adaptation to problems posed on complicated domains which may contain a huge number of local geometrical features, or micro-structures. Here, we exploit the composite variant of the discontinuous Galerkin finite element method based on exploiting finite element meshes consisting of arbitrarily shaped element domains. Adaptive mesh refinement is based on constructing finite element partitions of the domain consisting of agglomerated elements which belong to different levels of an underlying hierarchical tree data structure. As an example of the application of these techniques, we consider the numerical approximation of the incompressible Navier–Stokes equations. Numerical experiments highlighting the practical performance of the proposed refinement strategy will be presented.

Citation

Giani, S., & Houston, P. (2014). Goal-oriented adaptive composite discontinuous Galerkin methods for incompressible flows. Journal of Computational and Applied Mathematics, 270, 32-42. https://doi.org/10.1016/j.cam.2014.03.007

• Journal Article Type: Article
• Publication Date: Nov 1, 2014
• Deposit Date: Sep 29, 2014
• Journal: Journal of Computational and Applied Mathematics
• Print ISSN: 0377-0427
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 270
• Pages: 32-42
• DOI: https://doi.org/10.1016/j.cam.2014.03.007
• Keywords: Composite finite element methods, Discontinuous Galerkin methods, A posteriori error estimation, Adaptivity, Incompressible flows.