Optimal trace inequality constants for interior penalty discontinuous Galerkin discretisations of elliptic operators using arbitrary elements with non-constant Jacobians

DOI10.1016/j.jcp.2017.09.020zbMath1380.65387OpenAlexW2756385467MaRDI QIDQ1699056

J. Kópházi, A. R. Owens, Matthew D. Eaton

Publication date: 16 February 2018

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2017.09.020

zbMATH Keywords

finite element analysisdiscontinuous Galerkinisogeometric analysisinterior penaltydiffusion synthetic accelerationtrace inverse inequality

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items

NURBS Enhanced Virtual Element Methods for the Spatial Discretization of the Multigroup Neutron Diffusion Equation on Curvilinear Polygonal Meshes

Uses Software

• LAPACK
• Spalart-Allmaras

Cites Work

• Discontinuous diffusion synthetic acceleration for \(S_n\) transport on 2D arbitrary polygonal meshes
• What are \(C\) and \(h\)?: Inequalities for the analysis and design of finite element methods
• On the constants in \(hp\)-finite element trace inverse inequalities.
• An explicit expression for the penalty parameter of the interior penalty method
• Explicit trace inequalities for isogeometric analysis and parametric hexahedral finite elements
• On the stability of the symmetric interior penalty method for the Spalart-Allmaras turbulence model
• Dual-primal isogeometric tearing and interconnecting solvers for multipatch dG-Iga equations
• Estimation of penalty parameters for symmetric interior penalty Galerkin methods
• Discontinuous finite element methods for incompressible flows on subdomains with non-matching interfaces
• Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. (On a variational principle for solving Dirichlet problems less boundary conditions using subspaces)
• Numerical Methods for Large Eigenvalue Problems
• LAPACK Users' Guide
• An Interior Penalty Finite Element Method with Discontinuous Elements
• An Elliptic Collocation-Finite Element Method with Interior Penalties
• A finite element method for domain decomposition with non-matching grids
• Performance of Discontinuous Galerkin Methods for Elliptic PDEs
• Projected Krylov Methods for Saddle-Point Systems
• Piecewise Solenoidal Vector Fields and the Stokes Problem