A Nitsche-eXtended finite element method for distributed optimal control problems of elliptic interface equations
Numerical Analysis
2018-10-05 v1
Abstract
This paper analyzes an interface-unfitted numerical method for distributed optimal control problems governed by elliptic interface equations. We follow the variational discretization concept to discretize the optimal control problems, and apply a Nitsche-eXtended finite element method to discretize the corresponding state and adjoint equations, where piecewise cut basis functions around the interface are enriched into the standard linear element space. Optimal error estimates of the state, co-state and control in a mesh-dependent norm and the norm are derived. Numerical results are provided to verify the theoretical results.
Cite
@article{arxiv.1810.02271,
title = {A Nitsche-eXtended finite element method for distributed optimal control problems of elliptic interface equations},
author = {Tao Wang and Chaochao Yang and Xiaoping Xie},
journal= {arXiv preprint arXiv:1810.02271},
year = {2018}
}