Name
Abstract | ||
|---|---|---|
Some optimal design problems in topology optimization eventually lead to degenerate convex minimization problems \(E(v):=\int _\varOmega W(\nabla v)dx-\int _\varOmega fvdx\) for \(v\in H_{0}^{1}(\varOmega ) \) with possibly multiple minimizers u, but with a unique stress \(\sigma :=DW(\nabla u)\). The discretization of degenerate convex minimization problems experience numerical difficulties with a singular or nearly singular Hessian matrix. This paper studies a modified discretization by adding a stabilization term to the discrete energy. It will be proven that this stabilization technique leads to a posteriori error control on unstructured triangulations, and so enables the use of adaptive algorithms. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1007/s10915-017-0409-8 | J. Sci. Comput. |
Keywords | Field | DocType |
Adaptive finite element methods, Stabilization, A posteriori error estimates, Optimal design problem, 65N12, 65N30, 65Y20 | Degenerate energy levels,Discretization,Mathematical optimization,Nabla symbol,Mathematical analysis,Hessian matrix,Optimal design,Finite element method,Topology optimization,Convex optimization,Mathematics | Journal |
Volume | Issue | ISSN |
73 | 1 | 0885-7474 |
Citations | PageRank | References |
0 | 0.34 | 8 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| D. J. Liu | 1 | 0 | 0.34 |
| D. D. Jiang | 2 | 0 | 0.34 |
| Y. Liu | 3 | 0 | 0.34 |
| Q. Q. Xia | 4 | 0 | 0.34 |