A note on the devising of superconvergent HDG methods for Stokes flow by M-decompositions. (29th June 2016)

• Record Type: Journal Article
• Authors: Cockburn, Bernardo; Fu, Guosheng; Qiu, Weifeng
• Is Part Of: IMA journal of numerical analysis. Volume 37:Number 2(2017)
• Page Start: 730
• Page End: 749
• Publication Date: 2016-06-29
• Subjects: hybridization -- discontinuous Galerkin -- superconvergence -- Stokes flow -- M-decompositions.; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/drw029
• Languages: English
• ISSNs: 0272-4979

Abstract

Abstract : In this article, we to devise superconvergent hybridizable discontinuous Galerkin methods on unstructured polygonal/polyhedral meshes for the Stokes equations of incompressible fluid flow by using $M$ -decompositions. We do this for two formulations of the equations, namely, for the velocity gradient–velocity-pressure formulation, and for the more difficult strain rate–velocity-pressure formulation. We also show how to locally postprocess the approximate velocity to obtain a globally divergence-free and $H(\mathrm{div})$ -conforming velocity converging faster than the original approximate velocity.