Polynomial preserving recovery of an over-penalized symmetric interior penalty Galerkin method for elliptic problems

DOI10.3934/dcdsb.2015.20.1405zbMath1334.65185OpenAlexW2524476428MaRDI QIDQ256831

Zhimin Zhang, Lun-Ji Song

Publication date: 10 March 2016

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2015.20.1405

zbMATH Keywords

superconvergencea posteriori error estimatordiscrete least squares fittingsymmetric interior penalty Galerkin method

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) 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

Symmetric interior penalty Galerkin approaches for two-dimensional parabolic interface problems with low regularity solutions ⋮ Convergence of a second-order linearized BDF-IPDG for nonlinear parabolic equations with discontinuous coefficients ⋮ Superconvergence property of an over-penalized discontinuous Galerkin finite element gradient recovery method ⋮ Polynomial preserving recovery for a class of weak Galerkin finite element methods ⋮ A high-order symmetric interior penalty discontinuous Galerkin scheme to simulate vortex dominated incompressible fluid flow

Uses Software

• DistMesh

Cites Work

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• A posteriori error control for a weakly over-penalized symmetric interior penalty method
• A weakly over-penalized symmetric interior penalty method
• On a BPX-preconditioner for P1 elements
• Estimation of penalty parameters for symmetric interior penalty Galerkin methods
• The polynomial-preserving recovery for higher order finite element methods in 2D and 3D
• Continuous interior penalty $hp$-finite element methods for advection and advection-diffusion equations
• Polynomial preserving recovery for meshes from Delaunay triangulation or with high aspect ratio
• Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations
• Superconvergence of quadratic finite elements on mildly structured grids
• Some A Posteriori Error Estimators for Elliptic Partial Differential Equations
• A simple error estimator and adaptive procedure for practical engineerng analysis
• An Interior Penalty Finite Element Method with Discontinuous Elements
• The superconvergent patch recovery anda posteriori error estimates. Part 1: The recovery technique
• An Elliptic Collocation-Finite Element Method with Interior Penalties
• A‐posteriori error estimates for the finite element method
• A Simple Mesh Generator in MATLAB
• A Posteriori Error Estimates Based on the Polynomial Preserving Recovery
• Analysis of recovery type a posteriori error estimators for mildly structured grids
• A New Finite Element Gradient Recovery Method: Superconvergence Property