Paper Info
Title
A convergent adaptive finite element method for an optimal design problem
Abstract
The optimal design problem for maximal torsion stiffness of an infinite bar of given geometry and unknown distribution of two materials of prescribed amounts is one model example in topology optimisation. It eventually leads to a degenerate convex minimisation problem. The numerical analysis is therefore delicate for possibly multiple primal variables u but unique derivatives σ : =  DW(D u). Even fine a posteriori error estimates still suffer from the reliability-efficiency gap. However, it motivates a simple edge-based adaptive mesh-refining algorithm (AFEM) that is not a priori guaranteed to refine everywhere. Its convergence proof is therefore based on energy estimates and some refined convexity control. Numerical experiments illustrate even nearly optimal convergence rates of the proposed AFEM.
Year
DOI
Venue
2008
10.1007/s00211-007-0122-x
Numerische Mathematik
Keywords
Field
DocType
optimal convergence rate,numerical experiment,convergent adaptive finite element,optimal design problem,convergence proof,numerical analysis,d u,energy estimate,multiple primal variables u,proposed afem,convex minimisation problem,optimal design,adaptive mesh refinement
Convergence (routing),Mathematical optimization,Convexity,Finite element method,Optimal design,Minimisation (psychology),Rate of convergence,Adaptive algorithm,Numerical analysis,Mathematics
Journal
Volume
Issue
ISSN
108
3
0945-3245
Citations 
PageRank 
References 
7
0.71
11
Authors
2
Name
Order
Citations
PageRank
Sören Bartels135556.90
C Carstensen2944163.02