Nitsche-XFEM for optimal control problems governed by elliptic PDEs with interfaces
Numerical Analysis
2018-05-11 v1 Optimization and Control
Abstract
For the optimal control problem governed by elliptic equations with interfaces, we present a numerical method based on the Hansbo's Nitsche-XFEM. We followed the Hinze's variational discretization concept to discretize the continuous problem on a uniform mesh. We derive optimal error estimates of the state, co-state and control both in mesh dependent norm and L2 norm. In addition, our method is suitable for the model with non-homogeneous interface condition. Numerical results confirmed our theoretical results, with the implementation details discussed.
Cite
@article{arxiv.1805.03944,
title = {Nitsche-XFEM for optimal control problems governed by elliptic PDEs with interfaces},
author = {Tao Wang and Chaochao Yang and Xiaoping Xie},
journal= {arXiv preprint arXiv:1805.03944},
year = {2018}
}