Lowest-order equivalent nonstandard finite element methods for biharmonic plates
DOI10.1051/m2an/2021085zbMath1483.65177arXiv2102.08125OpenAlexW3131705640MaRDI QIDQ5034773
Neela Nataraj, Carsten Carstensen
Publication date: 21 February 2022
Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2102.08125
comparisondiscontinuous Galerkin methodbiharmonic problemMorley\textit{a priori} error estimatescompanion operatorbest-approximation\(C^0\) interior penaltyWOPSIP
Plates (74K20) 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)
Related Items (5)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- \(C^0\) interior penalty methods for fourth order elliptic boundary value problems on polygonal domains
- A weakly over-penalized symmetric interior penalty method for the biharmonic problem
- \(hp\)-version a priori error analysis of interior penalty discontinuous Galerkin finite element approximations to the biharmonic equation
- An introduction to Sobolev spaces and interpolation spaces
- \(hp\)-version interior penalty DGFEMs for the biharmonic equation
- Elliptic partial differential equations of second order
- 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
- Constants in discrete Poincaré and Friedrichs inequalities and discrete quasi-interpolation
- A Morley finite element method for the displacement obstacle problem of clamped Kirchhoff plates
- A priori and a posteriori error analysis of the Crouzeix-Raviart and Morley FEM with original and modified right-hand sides
- A discrete Helmholtz decomposition with morley finite element functions and the optimality of adaptive finite element schemes
- Guaranteed lower eigenvalue bounds for the biharmonic equation
- Computational survey on a posteriori error estimators for nonconforming finite element methods for the Poisson problem
- A unifying theory of a posteriori error control for nonconforming finite element methods
- A unifying theory of a posteriori finite element error control
- A Review of Unified A Posteriori Finite Element Error Control
- An a posteriori error indicator for discontinuous Galerkin approximations of fourth-order elliptic problems
- A new error analysis for discontinuous finite element methods for linear elliptic problems
- Fully discrete dynamic mesh discontinuous Galerkin methods for the Cahn-Hilliard equation of phase transition
- Morley finite element method for the eigenvalues of the biharmonic operator
- On the boundary value problem of the biharmonic operator on domains with angular corners
- Finite Element Methods for Elliptic Equations Using Nonconforming Elements
- Convergence of nonconforming multigrid methods without full elliptic regularity
- A Priori Error Analysis for the hp-Version of the Discontinuous Galerkin Finite Element Method for the Biharmonic Equation
- Quasi-Optimal Nonconforming Methods for Symmetric Elliptic Problems. I---Abstract Theory
- Axioms of Adaptivity with Separate Marking for Data Resolution
- Quasi-Optimal Nonconforming Methods for Symmetric Elliptic Problems. II---Overconsistency and Classical Nonconforming Elements
- Quasi-Optimal Nonconforming Methods for Symmetric Elliptic Problems. III---Discontinuous Galerkin and Other Interior Penalty Methods
- Explicit Error Estimates for Courant, Crouzeix-Raviart and Raviart-Thomas Finite Element Methods
- A priori and a posteriori error control of discontinuous Galerkin finite element methods for the von Kármán equations
- How to Prove the Discrete Reliability for Nonconforming Finite Element Methods
- Finite Elemente
- Discontinuous Galerkin methods for the biharmonic problem
- Comparison Results of NonstandardP2Finite Element Methods for the Biharmonic Problem
- Adaptive Morley FEM for the von Kármán Equations with Optimal Convergence Rates
This page was built for publication: Lowest-order equivalent nonstandard finite element methods for biharmonic plates
