A discrete Helmholtz decomposition with morley finite element functions and the optimality of adaptive finite element schemes

DOI10.1016/j.camwa.2014.07.019zbMath1362.65123OpenAlexW2048407683MaRDI QIDQ2397299

Yanyan Li

Publication date: 22 May 2017

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2014.07.019

zbMATH Keywords

optimalityMorley elementdiscrete Helmholtz decompositionKirchhoff-Love plate problem

Mathematics Subject Classification ID

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) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55)

Related Items (20)

Lowest-order equivalent nonstandard finite element methods for biharmonic plates ⋮ Adaptive Morley element algorithms for the biharmonic eigenvalue problem ⋮ A posteriori error analysis for a distributed optimal control problem governed by the von Kármán equations ⋮ Direct Guaranteed Lower Eigenvalue Bounds with Optimal a Priori Convergence Rates for the Bi-Laplacian ⋮ Quasi-optimal convergence rate for an adaptive hybridizable \(C^0\) discontinuous Galerkin method for Kirchhoff plates ⋮ Multigrid methods for Hellan-Herrmann-Johnson mixed method of Kirchhoff plate bending problems ⋮ Optimal multilevel adaptive FEM for the Argyris element ⋮ Nonconforming Virtual Elements for the Biharmonic Equation with Morley Degrees of Freedom on Polygonal Meshes ⋮ Unifying a posteriori error analysis of five piecewise quadratic discretisations for the biharmonic equation ⋮ Hierarchical Argyris finite element method for adaptive and multigrid algorithms ⋮ Preface ⋮ Morley FEM for a distributed optimal control problem governed by the von Kármán equations ⋮ Morley finite element method for the von Kármán obstacle problem ⋮ The adaptive Ciarlet-Raviart mixed method for biharmonic problems with simply supported boundary condition ⋮ A New Discretization for $m$th-Laplace Equations with Arbitrary Polynomial Degrees ⋮ A priori and a posteriori error analysis of the Crouzeix-Raviart and Morley FEM with original and modified right-hand sides ⋮ Residual-Based A Posteriori Error Estimates for $hp$-Discontinuous Galerkin Discretizations of 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 ⋮ Conforming and nonconforming finite element methods for biharmonic inverse source problem

Uses Software

• p1afem
• na14

Cites Work

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