TY - JOUR
T1 - On Finite Element Approximations to a Shape Gradient Flow in Shape Optimization of Elliptic Problems
AU - Liu , Chunxiao
AU - Zhu , Shengfeng
JO - Journal of Computational Mathematics
VL - 5
SP - 956
EP - 979
PY - 2023
DA - 2023/05
SN - 41
DO - http://doi.org/10.4208/jcm.2208-m2020-0142
UR - https://global-sci.org/intro/article_detail/jcm/21681.html
KW - Shape optimization, Shape gradient, Eulerian derivative, Finite element, Error estimate.
AB - <p style="text-align: justify;">Shape gradient flows are widely used in numerical shape optimization algorithms. We
investigate the accuracy and effectiveness of approximate shape gradients flows for shape
optimization of elliptic problems. We present convergence analysis with a priori error
estimates for finite element approximations of shape gradient flows associated with a distributed or boundary expression of Eulerian derivative. Numerical examples are presented
to verify theory and show that using the volume expression is effective for shape optimization with Dirichlet and Neumann boundary conditions.</p>