A Nonconforming Finite Element Approximation for the von Karman equations

DOI10.1051/m2an/2015052zbMath1375.74089arXiv1506.08958OpenAlexW2962713585MaRDI QIDQ2806040

Neela Nataraj, Gouranga Mallik

Publication date: 13 May 2016

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.08958

zbMATH Keywords

error estimatesplate bendingvon Kármán equationsMorley elementnon-linear

Mathematics Subject Classification ID

Plates (74K20) Finite element methods applied to problems in solid mechanics (74S05) 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) PDEs in connection with mechanics of deformable solids (35Q74) Semilinear elliptic equations (35J61)

Related Items (16)

A posteriori error analysis for a distributed optimal control problem governed by the von Kármán equations ⋮ Error estimates for the numerical approximation of a distributed optimal control problem governed by the von Kármán equations ⋮ A Mixed Finite Element Scheme for Biharmonic Equation with Variable Coefficient and von Kármán Equations ⋮ A Hybrid High-Order Method for Quasilinear Elliptic Problems of Nonmonotone Type ⋮ A space-time adaptive discontinuous Galerkin method for the numerical solution of the dynamic quasi-static von Kármán equations ⋮ Unified a priori analysis of four second-order FEM for fourth-order quadratic semilinear problems ⋮ Energy minimising configurations of pre-strained multilayers ⋮ An adaptive \(\mathrm{C}^0\) Interior penalty discontinuous Galerkin method and an equilibrated a posteriori error estimator for the von Kármán equations ⋮ A hybrid high-order method for a class of strongly nonlinear elliptic boundary value problems ⋮ Morley FEM for a distributed optimal control problem governed by the von Kármán equations ⋮ Morley finite element method for the von Kármán obstacle problem ⋮ Morley finite element methods for the stationary quasi-geostrophic equation ⋮ Hessian discretisation method for fourth-order semi-linear elliptic equations: applications to the von Kármán and Navier-Stokes models ⋮ Finite element methods: research in India over the last decade ⋮ A virtual element method for the von Kármán equations ⋮ Adaptive Morley FEM for the von Kármán Equations with Optimal Convergence Rates

Uses Software

• na14

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A nonconforming Morley finite element method for the fully nonlinear Monge-Ampère equation
• Hybrid finite element methods for the von Kármán equations
• On the numerical analysis of the Von Kármán equations: Mixed finite element approximation and continuation techniques
• A mixed finite element method for the solutions of the von Kármán equations
• Remarks around 50 lines of Matlab: short finite element implementation
• A Morley finite element method for the displacement obstacle problem of clamped Kirchhoff plates
• The Morley element for fourth order elliptic equations in any dimensions
• An existence theorem for the von Kármán equations
• 𝒞⁰ penalty methods for the fully nonlinear Monge-Ampère equation
• On the boundary value problem of the biharmonic operator on domains with angular corners
• A two-level additive Schwarz method for the Morley nonconforming element approximation of a nonlinear biharmonic equation
• The Best L² Norm Error Estimate of Lower Order Finite Element Methods for the Fourth Order Problem
• Forty Years of the Crouzeix‐Raviart element
• Finite Elemente
• On von Karman’s equations and the buckling of a thin elastic plate
• On von kármán's equations and the buckling of a thin elastic plate, I the clamped plate
• Von Kármán's equations and the buckling of a thin elastic plate, II plate with general edge conditions

This page was built for publication: A Nonconforming Finite Element Approximation for the von Karman equations