TY - JOUR
T1 - An Interface-Unfitted Finite Element Method for Elliptic Interface Optimal Control Problems
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 727
EP - 749
PY - 2019
DA - 2019/04
SN - 12
DO - http://doi.org/10.4208/nmtma.OA-2018-0031
UR - https://global-sci.org/intro/article_detail/nmtma/13128.html
KW - Interface equations, interface control, variational discretization concept, cut finite element method.
AB - <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>