Discontinuous Galerkin approximations in computational mechanics: hybridization, exact geometry and degree adaptivity

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. Exa...

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Vydané v:SN applied sciences Ročník 1; číslo 9; s. 1047
Hlavní autori: Giacomini, Matteo, Sevilla, Ruben
Médium: Journal Article Publikácia
Jazyk:English
Vydavateľské údaje: Cham Springer International Publishing 01.09.2019
Springer Nature B.V
Springer
Predmet:
Anàlisi numèrica
Applied and Technical Physics
Approximation
B spline functions
Chemistry/Food Science
Computational mechanics
Computer applications
Computing costs
Degree adaptivity
Earth Sciences
Electrostatic properties
Electrostatics
Engineering
Engineering: Adaptive Model
Environment
Exact geometry
Face-centered fnite volume
Finite element method
Fluid flow
Fluid-structure interaction
Galerkin method
Galerkin methods
Galerkin, Mètodes de
Hybridizable discontinuous Galerkin
Hybridization
Incompressible flow
Matemàtiques i estadística
Materials Science
Mathematical analysis
Mathematical models
Mesh and Resolution Techniques for Computationally-Demanding Problems in Simulation-Based Engineering
Methods
Mixed formulation
Modelització matemàtica
NURBS-enhanced fnite element
Partial differential equations
Polynomials
Research Article
Simulation
Superconvergence
Tensors
Viscous flow
Àrees temàtiques de la UPC
NURBS-enhanced finite element
Degree adaptivity
Exact geometry
Superconvergence
Face-centered finite volume
Mixed formulation
Hybridizable discontinuous Galerkin
ISSN:2523-3963, 2523-3971, 2523-3971
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Popis
Shrnutí: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. 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.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:2523-3963
2523-3971
2523-3971
DOI:10.1007/s42452-019-1065-4