Adaptive nonconforming Crouzeix-Raviart FEM for eigenvalue problems

DOI10.1090/S0025-5718-2014-02894-9zbMath1311.65136OpenAlexW2012900529MaRDI QIDQ5179215

Carsten Carstensen, Dietmar Gallistl, Mira Schedensack

Publication date: 19 March 2015

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-2014-02894-9

zbMATH Keywords

algorithmconvergenceLaplace operatoreigenvalue boundfinite element method (FEM)

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) 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) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (24)

A natural nonconforming FEM for the Bingham flow problem is quasi-optimal ⋮ Direct Guaranteed Lower Eigenvalue Bounds with Optimal a Priori Convergence Rates for the Bi-Laplacian ⋮ Nonstandard finite element methods. Abstracts from the workshop held January 10--16, 2021 (hybrid meeting) ⋮ Axioms of adaptivity ⋮ A priori and a posteriori error analysis of the lowest-order NCVEM for second-order linear indefinite elliptic problems ⋮ Convergence and optimality of adaptive multigrid method for multiple eigenvalue problems ⋮ A discrete Helmholtz decomposition with morley finite element functions and the optimality of adaptive finite element schemes ⋮ Convergent adaptive hybrid higher-order schemes for convex minimization ⋮ Nonconforming Virtual Elements for the Biharmonic Equation with Morley Degrees of Freedom on Polygonal Meshes ⋮ Adaptive guaranteed lower eigenvalue bounds with optimal convergence rates ⋮ Two discretisations of the time-dependent Bingham problem ⋮ Unifying a posteriori error analysis of five piecewise quadratic discretisations for the biharmonic equation ⋮ Three First-Order Finite Volume Element Methods for Stokes Equations under Minimal Regularity Assumptions ⋮ Optimal convergence of adaptive FEM for eigenvalue clusters in mixed form ⋮ Optimal Convergence Rates for Adaptive Lowest-Order Discontinuous Petrov--Galerkin Schemes ⋮ An adaptive least-squares FEM for the Stokes equations with optimal convergence rates ⋮ Lower and upper bounds of Laplacian eigenvalue problem by weak Galerkin method on triangular meshes ⋮ A priori and a posteriori error analysis of the Crouzeix-Raviart and Morley FEM with original and modified right-hand sides ⋮ Guaranteed lower bounds on eigenvalues of elliptic operators with a hybrid high-order method ⋮ Taylor--Hood Discretization of the Reissner--Mindlin Plate ⋮ Adaptive Morley FEM for the von Kármán Equations with Optimal Convergence Rates ⋮ Conforming and nonconforming finite element methods for biharmonic inverse source problem ⋮ Comparison results for the Stokes equations ⋮ An optimal adaptive FEM for eigenvalue clusters

Cites Work

• Unnamed Item
• Unnamed Item
• A posteriori error estimates for non-conforming approximation of eigenvalue problems
• On the error bounds of nonconforming finite elements
• An oscillation-free adaptive FEM for symmetric eigenvalue problems
• An a posteriori error estimate and a comparison theorem for the nonconforming \(P_{1}\) element
• An optimally convergent adaptive mixed finite element method
• Convergence and optimal complexity of adaptive finite element eigenvalue computations
• Convergence of a standard adaptive nonconforming finite element method with optimal complexity
• Adaptive finite element methods with convergence rates
• Optimal adaptive nonconforming FEM for the Stokes problem
• Convergence and optimality of the adaptive nonconforming linear element method for the Stokes problem
• A natural adaptive nonconforming FEM of quasi-optimal complexity
• Optimality of a standard adaptive finite element method
• Convergence analysis of an adaptive nonconforming finite element method
• A Review of Unified A Posteriori Finite Element Error Control
• Finite element approximation of eigenvalue problems
• An Adaptive Finite Element Eigenvalue Solver of Asymptotic Quasi-Optimal Computational Complexity
• The Adaptive Nonconforming FEM for the Pure Displacement Problem in Linear Elasticity is Optimal and Robust
• A Convergent Nonconforming Adaptive Finite Element Method with Quasi-Optimal Complexity
• Quasi-Optimality of Adaptive Nonconforming Finite Element Methods for the Stokes Equations
• A new error analysis for discontinuous finite element methods for linear elliptic problems
• Guaranteed lower bounds for eigenvalues
• Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
• Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method
• Convergence and quasi-optimal complexity of a simple adaptive finite element method
• A Convergent Adaptive Algorithm for Poisson’s Equation
• Two-level additive Schwarz preconditioners for nonconforming finite element methods
• Comparison Results of Finite Element Methods for the Poisson Model Problem
• Explicit Error Estimates for Courant, Crouzeix-Raviart and Raviart-Thomas Finite Element Methods
• The completion of locally refined simplicial partitions created by bisection
• The Mathematical Theory of Finite Element Methods
• Finite Elements

This page was built for publication: Adaptive nonconforming Crouzeix-Raviart FEM for eigenvalue problems