A convergent adaptive finite element method for an optimal design problem
From MaRDI portal
Publication:2471692
DOI10.1007/s00211-007-0122-xzbMath1144.74038OpenAlexW2023040159MaRDI QIDQ2471692
Carsten Carstensen, Sören Bartels
Publication date: 18 February 2008
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: http://edoc.hu-berlin.de/18452/3400
Numerical optimization and variational techniques (65K10) 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)
Related Items
Justification of the saturation assumption, Adaptive Least-Squares, Discontinuous Petrov-Galerkin, and Hybrid High-Order Methods, Numerical Algorithms for the Simulation of Finite Plasticity with Microstructures, 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, Unstabilized Hybrid High-order Method for a Class of Degenerate Convex Minimization Problems, Nonconforming FEMs for an Optimal Design Problem
Cites Work
- Unnamed Item
- Analysis and numerical studies of a problem of shape design
- Numerical study of a relaxed variational problem from optimal design
- Adaptive finite element methods for microstructures? Numerical experiments for a 2-well benchmark
- Variational methods for structural optimization
- Convergent adaptive finite elements for the nonlinear Laplacian
- Convergence for stabilisation of degenerately convex minimisation problems
- Adaptive finite element methods with convergence rates
- Optimality of a standard adaptive finite element method
- On the Convergence of Finite-Element Approximations of a Relaxed Variational Problem
- Optimal design and relaxation of variational problems, I
- Numerical solution of the scalar double-well problem allowing microstructure
- Numerical Analysis of Compatible Phase Transitions in Elastic Solids
- Data Oscillation and Convergence of Adaptive FEM
- Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part I: Low order conforming, nonconforming, and mixed FEM
- Local Stress Regularity in Scalar Nonconvex Variational Problems
- Local problems on stars: A posteriori error estimators, convergence, and performance
- A Convergent Adaptive Algorithm for Poisson’s Equation
- Convergence of Adaptive Finite Element Methods for General Second Order Linear Elliptic PDEs
- Shape optimization by the homogenization method