TY - CHAP
T1 - Advanced numerical methods for pde constrained optimization with application to optimal design in navier stokes flow
AU - Brandenburg, Christian
AU - Lindemann, Florian
AU - Ulbrich, Michael
AU - Ulbrich, Stefan
N1 - Publisher Copyright:
© 2012, Springer Basel AG.
PY - 2012
Y1 - 2012
N2 - We present an approach to shape optimization which is based on transformation to a reference domain with continuous adjoint computations. This method is applied to the instationary Navier-Stokes equations for which we discuss the appropriate setting and discuss Fréchet differentiability of the velocity field with respect to domain transformations. Goal-oriented error estimation is used for an adaptive refinement strategy. Finally, we give some numerical results.
AB - We present an approach to shape optimization which is based on transformation to a reference domain with continuous adjoint computations. This method is applied to the instationary Navier-Stokes equations for which we discuss the appropriate setting and discuss Fréchet differentiability of the velocity field with respect to domain transformations. Goal-oriented error estimation is used for an adaptive refinement strategy. Finally, we give some numerical results.
KW - Goal-oriented error estimation
KW - Navier-Stokes equations
KW - Pde-constrained optimization
KW - Shape optimization
UR - https://www.scopus.com/pages/publications/85089905677
U2 - 10.1007/978-3-0348-0133-1_14
DO - 10.1007/978-3-0348-0133-1_14
M3 - Chapter
AN - SCOPUS:85089905677
T3 - International Series of Numerical Mathematics
SP - 257
EP - 275
BT - International Series of Numerical Mathematics
PB - Springer
ER -