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arXiv · 1805.04844

An interface-unfitted finite element method for elliptic interface optimal control problem

Chao Chao Yang·Tao Wang·Xiaoping Xie
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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 $L^2$ 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.

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Chao Chao Yang, Tao Wang, Xiaoping Xie. 2018-05-13. An interface-unfitted finite element method for elliptic interface optimal control problem. https://arxiv.org/abs/1805.04844

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