descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 07 Feb 2018Embargo end date: 01 Jan 2018 United Kingdom English Publisher:Springer Science and Business Media LLCJournal:Journal of Scientific Computing, volume 77, pages 1,953-1,980 (issn: 0885-7474, eissn: 1573-7691,

Authors: Sevilla Cárdenas, Rubén; Huerta, Antonio;

doi: 10.1007/s10915-018-0657-2 , 10.48550/arxiv.1801.06666

arXiv: 1801.06666

handle: 2117/117357

HDG-NEFEM with Degree Adaptivity for Stokes Flows

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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.

36 pages, 37 figures

Country

United Kingdom

Related Organizations

Universitat Politècnica de Catalunya
Spain
Universitat Polite`cnica de Catalunya
Spain
Swansea University
United Kingdom

Keywords

Difference equations, Engineering, Civil, Classificació AMS::65 Numerical analysis::65N Partial differential equations, boundary value problems, Stokes, Engineering, Multidisciplinary, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Numerical solution of discretized equations for boundary value problems involving PDEs, Difference equations, Partial--Numerical solutions, :65 Numerical analysis::65N Partial differential equations, boundary value problems [Classificació AMS], Classificació AMS::65 Numerical analysis::65N Partial differential equations, boundary value problems, Stokes and related (Oseen, etc.) flows, Numerical computation using splines, :Matemàtiques i estadística::Anàlisi numèrica [Àrees temàtiques de la UPC], hybridisable discontinuous Galerkin, FOS: Mathematics, 65N08, 65N12, 65N22, 65N30, NURBS-enhanced finite element method, Reduced Order Models, Engineering, Ocean, Mathematics - Numerical Analysis, Engineering, Aerospace, Engineering, Biomedical, Domain Decomposition, Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica, degree adaptivity, Numerical Analysis (math.NA), Stability and convergence of numerical methods for boundary value problems involving PDEs, Computer Science, Software Engineering, Engineering, Marine, Proper Generalized Decomposition, Equacions diferencials parcials--solucions numèriques, Partial--Numerical solutions, Engineering, Manufacturing, Engineering, Mechanical, Engineering, Industrial, Parameterized solutions, Finite element methods applied to problems in fluid mechanics

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