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Title:
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Discontinuous Galerkin approximations in computational mechanics: hybridization, exact geometry and degree adaptivity
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Author:
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Giacomini, Matteo; Sevilla Cárdenas, Rubén
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Other authors:
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Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria |
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Abstract:
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Discontinuous Galerkin (DG) discretizations with exact representation of the geometry and local polynomial degree adaptivity are revisited. Hybridization techniques are employed to reduce the computational cost of DG approximations and devise the hybridizable discontinuous Galerkin (HDG) method. Exact geometry described by non-uniform rational B-splines (NURBS) is integrated into HDG using the framework of the NURBS-enhanced finite element method (NEFEM). Moreover, optimal convergence and superconvergence properties of HDG-Voigt formulation in presence of symmetric second-order tensors are exploited to construct inexpensive error indicators and drive degree adaptive procedures. Applications involving the numerical simulation of problems in electrostatics, linear elasticity and incompressible viscous flows are presented. Moreover, this is done for both high-order HDG approximations and the lowest-order framework of face-centered finite volumes (FCFV). |
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Abstract:
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Peer Reviewed |
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Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Modelització matemàtica
-Galerkin methods
-Hybridizable discontinuous Galerkin
-Mixed formulation
-Exact geometry
-NURBS-enhanced fnite
element
-Degree adaptivity
-Superconvergence
-Face-centered fnite volume
-Galerkin, Mètodes de |
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Rights:
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Document type:
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Article - Submitted version
Article |
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Published by:
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Springer
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