An Adaptive Least-Squares FEM for Linear Elasticity with Optimal Convergence Rates

DOI10.1137/16M1083797zbMath1462.65179OpenAlexW2786498193MaRDI QIDQ4603035

Gerhard Starke, Carsten Carstensen, Philipp Bringmann

Publication date: 14 February 2018

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/16m1083797

zbMATH Keywords

adaptive finite element methodoptimal convergence ratesleast-squares finite element methodsuperclosenessseparate markinglinear, elasticity

Mathematics Subject Classification ID

Classical linear elasticity (74B05) 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) Complexity and performance of numerical algorithms (65Y20)

Related Items (10)

Adaptive Least-Squares, Discontinuous Petrov-Galerkin, and Hybrid High-Order Methods ⋮ \(h\)-adaptive least-squares finite element methods for the 2D Stokes equations of any order with optimal convergence rates ⋮ Axioms of Adaptivity with Separate Marking for Data Resolution ⋮ How to prove optimal convergence rates for adaptive least-squares finite element methods ⋮ A short note on plain convergence of adaptive least-squares finite element methods ⋮ Optimal Convergence Rates for Adaptive Lowest-Order Discontinuous Petrov--Galerkin Schemes ⋮ Collective marking for arbitrary order adaptive least-squares finite element methods with optimal rates ⋮ Adaptive Mixed Finite Element Methods for Non-self-adjoint Indefinite Second-Order Elliptic PDEs with Optimal Rates ⋮ Collective marking for adaptive least-squares finite element methods with optimal rates ⋮ Further results on a space-time FOSLS formulation of parabolic PDEs

Cites Work

• Unnamed Item
• Unnamed Item
• Axioms of adaptivity
• An adaptive least-squares FEM for the Stokes equations with optimal convergence rates
• Mollification in strongly Lipschitz domains with application to continuous and discrete de Rham complexes
• Least-squares finite element methods
• Mixed finite elements in \(\mathbb{R}^3\)
• Éléments finis mixtes incompressibles pour l'équation de Stokes dans \(R^ 3\).
• Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
• Analysis of the edge finite element approximation of the Maxwell equations with low regularity solutions
• Fast computation in adaptive tree approximation
• Adaptive finite element methods with convergence rates
• Convergence of natural adaptive least squares finite element methods
• Convergence and Optimality of Adaptive Least Squares Finite Element Methods
• An optimal adaptive mixed finite element method
• A note on least-squares mixed finite elements in relation to standard and mixed finite elements
• Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
• Finite Element Methods for Navier-Stokes Equations
• Axioms of Adaptivity with Separate Marking for Data Resolution
• Least-Squares Methods for Linear Elasticity
• Mixed Finite Element Methods and Applications
• Explicit Error Estimates for Courant, Crouzeix-Raviart and Raviart-Thomas Finite Element Methods
• Finite Elemente
• Convergence and optimality of adaptive edge finite element methods for time-harmonic Maxwell equations
• The completion of locally refined simplicial partitions created by bisection
• The Mathematical Theory of Finite Element Methods
• A posteriori error estimates for Maxwell equations

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