@Article{NMTMA-12-727,
author = {Chaochao Yang, Tao Wang and Xiaoping Xie},
title = {An Interface-Unfitted Finite Element Method for Elliptic Interface Optimal Control Problems},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2019},
volume = {12},
number = {3},
pages = {727--749},
abstract = {<p style="text-align: justify;">This paper develops and analyses numerical approximation for linear-quadratic
optimal control problems governed by elliptic interface equations. We adopt variational
discretization concept to discretize optimal control problems, and apply an interface-unfitted finite element method due to [A. Hansbo and P. Hansbo. An unfitted finite
element method, based on Nitsche&#39;s method, for elliptic interface problems. Comput.
Methods Appl. Mech. Engrg., 191(47-48): 5537-5552, 2002] to discretize the corresponding state and adjoint equations, where piecewise cut basis functions around interface are enriched into standard conforming finite element space. Optimal error estimates in both $L$<sup>2</sup> norm and a mesh-dependent norm are derived for the optimal state,
co-state and control under different regularity assumptions. Numerical results verify the
theoretical results.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2018-0031},
url = {http://global-sci.org/intro/article_detail/nmtma/13128.html}
}