The \(L^{2}\)-optimality of the IIPG method for odd degrees of polynomial approximation in 1D

DOI10.1007/s10915-009-9319-8zbMath1203.65251OpenAlexW2092171993MaRDI QIDQ618557

Oto Havle, Vít Dolejší

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/s10915-009-9319-8

zbMATH Keywords

error estimatesincomplete interior penalty Galerkin methododd polynomial approximations

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items

L ² -estimates for the DG IIPG-0 scheme, Some nonstandard error analysis of discontinuous Galerkin methods for elliptic problems, A Sequential Least Squares Method for Poisson Equation Using a Patch Reconstructed Space, An unfitted finite element method by direct extension for elliptic problems on domains with curved boundaries and interfaces

Cites Work

• Sub-optimal convergence of non-symmetric discontinuous Galerkin methods for odd polynomial approximations
• Compatible algorithms for coupled flow and transport
• Analysis of a family of discontinuous Galerkin methods for elliptic problems: the one dimensional case
• A discontinuous \(hp\) finite element method for diffusion problems: 1-D analysis
• Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. I
• Analysis of the discontinuous Galerkin method for nonlinear convection--diffusion problems
• Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations
• An Interior Penalty Finite Element Method with Discontinuous Elements
• Poincaré--Friedrichs Inequalities for Piecewise H¹ Functions
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• Unnamed Item
• Unnamed Item