Volume 12, Issue 3
An Interface-Unfitted Finite Element Method for Elliptic Interface Optimal Control Problems

Chaochao Yang ,  Tao Wang and Xiaoping Xie

10.4208/nmtma.OA-2018-0031

Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 727-749.

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  • Abstract

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 interfaceunfitted 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 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 L2 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.

  • History

Published online: 2019-04

  • AMS Subject Headings

49J20, 49M25, 65N12, 65N30

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