Residual-Based A Posteriori Error Estimates for $hp$-Discontinuous Galerkin Discretizations of the Biharmonic Problem
DOI10.1137/20M1364114zbMath1473.65297arXiv2009.14140MaRDI QIDQ4989948
Zhaonan Dong, Oliver J. Sutton, Lorenzo Mascotto
Publication date: 27 May 2021
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2009.14140
adaptivitydiscontinuous Galerkin methodsa posteriori error analysispolynomial inverse estimatesfourth-order PDEs\(hp\)-Galerkin methods
Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30)
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Cites Work
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- \(C^0\) interior penalty methods for fourth order elliptic boundary value problems on polygonal domains
- Mixed discontinuous Galerkin finite element method for the biharmonic equation
- A posteriori error estimates for continuous/discontinuous Galerkin approximations of the Kirchhoff-love plate
- A posteriori error estimates for the Morley plate bending element
- \(hp\)-version a priori error analysis of interior penalty discontinuous Galerkin finite element approximations to the biharmonic equation
- A new a posteriori error estimate for the Morley element
- \(hp\)-version interior penalty DGFEMs for the biharmonic equation
- On the constants in \(hp\)-finite element trace inverse inequalities.
- A posteriori error estimates for fourth-order elliptic problems
- Exponential convergence of \(hp\)-FEM for elliptic problems in polyhedra: mixed boundary conditions and anisotropic polynomial degrees
- A posteriori error estimates for nonconforming finite element methods
- Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates, and strain gradient elasticity
- Mathematical analysis of thin plate models
- Convergence rates of AFEM with \(H^{-1}\) data
- Local high-order regularization and applications to \(hp\)-methods
- \(hp\)-FEM for a stabilized three-field formulation of the biharmonic problem
- Virtual enriching operators
- A discrete Helmholtz decomposition with morley finite element functions and the optimality of adaptive finite element schemes
- Discrete Miranda-Talenti estimates and applications to linear and nonlinear PDEs
- An error indicator for mortar element solutions to the Stokes problem
- An a posteriori error indicator for discontinuous Galerkin approximations of fourth-order elliptic problems
- A Family of ${C}^0$ Finite Elements For Kirchhoff Plates I: Error Analysis
- An a posteriori error estimator for a quadratic C0-interior penalty method for the biharmonic problem
- A posteriori error analysis for the Morley plate element with general boundary conditions
- The $h-p$ version of the finite element method with quasiuniform meshes
- A family of $C^1$ finite elements with optimal approximation properties for various Galerkin methods for 2nd and 4th order problems
- Finite Element Methods for Elliptic Equations Using Nonconforming Elements
- Elliptic Reconstruction and a Posteriori Error Estimates for Parabolic Problems
- A Priori Error Analysis for the hp-Version of the Discontinuous Galerkin Finite Element Method for the Biharmonic Equation
- Stabilizedhp-Finite Element Methods for First-Order Hyperbolic Problems
- Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
- Polynomial robust stability analysis for $H$(div)-conforming finite elements for the Stokes equations
- A posteriori error estimators for nonconforming finite element methods
- Mixed Finite Element Methods and Applications
- Unified analysis of discontinuous Galerkin andC0-interior penalty finite element methods for Hamilton–Jacobi–Bellman and Isaacs equations
- Discontinuous Galerkin Methods for the Biharmonic Problem on Polygonal and Polyhedral Meshes
- Discontinuous Galerkin methods for the biharmonic problem
- hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes
- The Mathematical Theory of Finite Element Methods
- hp-Interpolation of Nonsmooth Functions and an Application to hp-A posteriori Error Estimation
- On residual-based a posteriori error estimation in hp-FEM
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