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HDG-NEFEM with Degree Adaptivity for Stokes Flows / Ruben Sevilla; Antonio Huerta

Journal of Scientific Computing

Swansea University Author: Sevilla, Ruben

Abstract

The NURBS-enhanced finite element method (NEFEM) combined with a hybridisable discontinuous Galerkin (HDG) approach is presented for the first time. The proposed technique completely eliminates the uncertainty induced by a polynomial approximation of curved boundaries that is common within an isopar...

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Published in: Journal of Scientific Computing
ISSN: 0885-7474 1573-7691
Published: 2018
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa38254
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Abstract: The NURBS-enhanced finite element method (NEFEM) combined with a hybridisable discontinuous Galerkin (HDG) approach is presented for the first time. The proposed technique completely eliminates the uncertainty induced by a polynomial approximation of curved boundaries that is common within an isoparametric approach and, compared to other DG methods, provides a significant reduction in number of degrees of freedom. In addition, by exploiting the ability of HDG to compute a postprocessed solution and by using a local a priori error estimate valid for elliptic problems, an inexpensive, reliable and computable error estimator is devised. The proposed methodology is used to solve Stokes flow problems using automatic degree adaptation. Particular attention is paid to the importance of an accurate boundary representation when changing the degree of approximation in curved elements. Several strategies are compared and the superiority and reliability of HDG-NEFEM with degree adaptation is illustrated.
Keywords: Hybridisable discontinuous Galerkin, NURBS-enhanced finite element method, Degree adaptivity, Stokes
College: College of Engineering