On the suboptimality of the \(p\)-version interior penalty discontinuous Galerkin method

DOI10.1007/s10915-009-9315-zzbMath1203.65253OpenAlexW2118468229MaRDI QIDQ618550

Jens Markus Melenk, Emmanuil H. Georgoulis, Edward J. C. Hall

Publication date: 16 January 2011

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-009-9315-z

zbMATH Keywords

discontinuous Galerkin method\(p\)-versioninterior penaltysuboptimalitya priori error estimation

Mathematics Subject Classification ID

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

Related Items

ℎ𝑝-Optimal discontinuous Galerkin methods for linear elliptic problems, Interpolation in Jacobi-weighted spaces and its application to a posteriori error estimations of the \(p\)-version of the finite element method, Discontinuous Galerkin Methods for Linear Problems: An Introduction, On the stability of the boundary trace of the polynomial \(L^2\)-projection on triangles and tetrahedra, Convergence analysis of a hp‐finite element approximation of the time‐harmonic Maxwell equations with impedance boundary conditions in domains with an analytic boundary, \(hp\)-optimal interior penalty discontinuous Galerkin methods for the biharmonic problem, General DG-methods for highly indefinite Helmholtz problems, Hypocoercivity-compatible Finite Element Methods for the Long-time Computation of Kolmogorov's Equation, Interior penalty discontinuous Galerkin FEMs for a gradient beam and cnts, An adaptive high-order unfitted finite element method for elliptic interface problems, A hybridizable discontinuous triangular spectral element method on unstructured meshes and its \textit{hp}-error estimates

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• An introduction to Sobolev spaces and interpolation spaces
• The h, p and h-p versions of the finite element method in 1 dimension. I. The error analysis of the p-version
• 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)
• ℎ𝑝-Optimal discontinuous Galerkin methods for linear elliptic problems
• Approximation Results for Orthogonal Polynomials in Sobolev Spaces
• The Optimal Convergence Rate of the p-Version of the Finite Element Method
• The Finite Element Method with Penalty
• A Priori Error Estimates for Finite Element Methods Based on Discontinuous Approximation Spaces for Elliptic Problems
• Direct and Inverse Approximation Theorems for the p-Version of the Finite Element Method in the Framework of Weighted Besov Spaces. Part I: Approximability of Functions in the Weighted Besov Spaces
• Discontinuoushp-Finite Element Methods for Advection-Diffusion-Reaction Problems
• Optimal error estimates for the hp-version interior penalty discontinuous Galerkin finite element method