Finite Element Discretization in Shape Optimization Problems for the Stationary Navier-Stokes Equation

Tiba, Dan

doi:10.1007/978-3-642-36062-6_44

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Theorem 26 Any Accumulation Point In the Hausdorff-pompeiu C...1

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“…In [60], the case of the Dirichlet boundary conditions under the Sverak compactness condition [59] is analyzed, while [101] extends theorem 26 to stationary Navier-Stokes systems with Dirichlet conditions. Note that, in particular, theorem 26 gives an existence result for the continuous problem (37), (19), (20) on O.…”

Section: Theorem 26 Any Accumulation Point In the Hausdorff-pompeiu C...mentioning

confidence: 99%

Fixed domain approaches in shape optimization problems

Neittaanmäki

Tiba

2012

Inverse Problems

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This work is a review of results in the approximation of optimal design problems, defined in variable/unknown domains, based on associated optimization problems defined in a fixed 'hold-all' domain, including the family of all admissible open sets. The literature in this respect is very rich and we concentrate on three main approaches: penalization-regularization, finite element discretization on a fixed grid, controllability and control properties of elliptic systems. Comparison with other fixed domain approaches or, in general, with other methods in shape optimization is performed as well and several numerical examples are included.

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