Volume 5, Issue 1
An Adaptive Finite Element Method for Shape Optimization in Stationary Incompressible Flow with Damp

Jian Su, Zhangxin Chen, Zhiheng Wang & Guang Xi

DOI:

Int. J. Numer. Anal. Mod. B, 5 (2014), pp. 79-96

Published online: 2014-05

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  • Abstract

This paper develops an adaptive finite element method for shape optimization in stationary incompressible flow with damping. The continuous shape gradient of an objective functional with respect to the boundary shape is derived by using the adjoint equation method and a function space parametrization technique. A projection a-posteriori error estimator is proposed, which can be computed easily and implemented in parallel. Based on this error estimator, an adaptive finite element method is constructed to solve state and adjoint equations and a regularized equation in each iteration step. Finally, the effectiveness of this adaptive method is demonstrated by numerical experiments.

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@Article{IJNAMB-5-79, author = {Jian Su, Zhangxin Chen, Zhiheng Wang and Guang Xi}, title = {An Adaptive Finite Element Method for Shape Optimization in Stationary Incompressible Flow with Damp}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2014}, volume = {5}, number = {1}, pages = {79--96}, abstract = {This paper develops an adaptive finite element method for shape optimization in stationary incompressible flow with damping. The continuous shape gradient of an objective functional with respect to the boundary shape is derived by using the adjoint equation method and a function space parametrization technique. A projection a-posteriori error estimator is proposed, which can be computed easily and implemented in parallel. Based on this error estimator, an adaptive finite element method is constructed to solve state and adjoint equations and a regularized equation in each iteration step. Finally, the effectiveness of this adaptive method is demonstrated by numerical experiments.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/221.html} }
TY - JOUR T1 - An Adaptive Finite Element Method for Shape Optimization in Stationary Incompressible Flow with Damp AU - Jian Su, Zhangxin Chen, Zhiheng Wang & Guang Xi JO - International Journal of Numerical Analysis Modeling Series B VL - 1 SP - 79 EP - 96 PY - 2014 DA - 2014/05 SN - 5 DO - http://dor.org/ UR - https://global-sci.org/intro/article_detail/ijnamb/221.html KW - AB - This paper develops an adaptive finite element method for shape optimization in stationary incompressible flow with damping. The continuous shape gradient of an objective functional with respect to the boundary shape is derived by using the adjoint equation method and a function space parametrization technique. A projection a-posteriori error estimator is proposed, which can be computed easily and implemented in parallel. Based on this error estimator, an adaptive finite element method is constructed to solve state and adjoint equations and a regularized equation in each iteration step. Finally, the effectiveness of this adaptive method is demonstrated by numerical experiments.
Jian Su, Zhangxin Chen, Zhiheng Wang & Guang Xi. (1970). An Adaptive Finite Element Method for Shape Optimization in Stationary Incompressible Flow with Damp. International Journal of Numerical Analysis Modeling Series B. 5 (1). 79-96. doi:
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