An Interface-Unfitted Finite Element Method for Elliptic Interface Optimal Control Problems

An Interface-Unfitted Finite Element Method for Elliptic Interface Optimal Control Problems

Year:    2019

Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 3 : pp. 727–749

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 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 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 $L$2 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2018-0031

Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 3 : pp. 727–749

Published online:    2019-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

Keywords:    Interface equations interface control variational discretization concept cut finite element method.

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