An interface-unfitted finite element method for elliptic interface optimal control problem
Abstract
This paper develops and analyses numerical approximation for linear-quadratic optimal control problem governed by elliptic interface equations. We adopt variational discretization concept to discretize optimal control problem, and apply an interface-unfitted finite element method due to [A. Hansbo and P. Hansbo. An unfitted finite element method, based on Nitsche's method, for elliptic interface problems. Comput. Methods Appl. Mech. Engrg., 191(47-48): 5537-5552, 2002] to discretize 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 norm and a mesh-dependent norm are derived for optimal state, co-state and control under different regularity assumptions. Numerical results verify the theoretical results.
Cite
@article{arxiv.1805.04844,
title = {An interface-unfitted finite element method for elliptic interface optimal control problem},
author = {Chao Chao Yang and Tao Wang and Xiaoping Xie},
journal= {arXiv preprint arXiv:1805.04844},
year = {2018}
}