Nonconforming FEMs for an Optimal Design Problem

DOI10.1137/130927103zbMath1312.74036OpenAlexW2071552456MaRDI QIDQ5253595

Carsten Carstensen, Dongjie Liu

Publication date: 27 May 2015

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

Full work available at URL: https://semanticscholar.org/paper/e3dc66b8a22e6f359a250d54af69c28f9cb539ca

zbMATH Keywords

finite element methodoptimal design problemnonconformingRaviart-ThomasCrouzeix-Raviartdual energyreliability-efficiency gaptwo-sided energy estimates

Mathematics Subject Classification ID

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) Topological methods for optimization problems in solid mechanics (74P15) Complexity and performance of numerical algorithms (65Y20)

Related Items (14)

Adaptive Least-Squares, Discontinuous Petrov-Galerkin, and Hybrid High-Order Methods ⋮ Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap ⋮ Convergent adaptive hybrid higher-order schemes for convex minimization ⋮ Stabilized FEM for some optimal design problem ⋮ Explicit and efficient error estimation for convex minimization problems ⋮ Relaxed Kačanov Scheme for the \(\boldsymbol{p}\)-Laplacian with Large Exponent ⋮ The Discrete Raviart-Thomas Mixed Finite Element Method for the $P$-Laplace Equation ⋮ Crouzeix-Raviart approximation of the total variation on simplicial meshes ⋮ Approximating the total variation with finite differences or finite elements ⋮ Nonconforming FEMs for the $p$-Laplace Problem ⋮ Nonconforming discretizations of convex minimization problems and precise relations to mixed methods ⋮ Orthogonality relations of Crouzeix-Raviart and Raviart-Thomas finite element spaces ⋮ The adaptive finite element method for the \(p\)-Laplace problem ⋮ Unstabilized Hybrid High-order Method for a Class of Degenerate Convex Minimization Problems

Uses Software

• mfem

Cites Work

• Axioms of adaptivity
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• The Mathematical Theory of Finite Element Methods
• Convex Analysis
• Three Matlab Implementations of the Lowest-order Raviart-Thomas Mfem with a Posteriori Error Control

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