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Numerical Algorithms
Published in: Numerical Algorithms 1/2020

13-06-2019 | Original Paper

Unfitted finite element for optimal control problem of the temperature in composite media with contact resistance

Authors: Qian Zhang, Tengjin Zhao, Zhiyue Zhang

Published in: Numerical Algorithms | Issue 1/2020

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Abstract

This paper presents a numerical method for the optimal control problem governed by the heat diffusion equation inside a composite medium. The contact resistance at the interface of constitute materials allows for jumps of the temperature field. The derivation process of the Karush-Kuhn-Tucher system is given by the formal Lagrange method. Due to the discontinuity of the temperature field, the standard linear finite element method cannot achieve optimal convergence when the uniform mesh is used. Therefore, the unfitted finite element method is applied to discrete the state equation required in the variational discretization approach. Optimal error estimates in the broken H1-norm and L2-norm for the control, state, and adjoint state are derived. Some numerical examples are provided to confirm the theoretical results.
previous article A finite difference approximation of reduced coupled model for slightly compressible Forchheimer fractures in Karst aquifer system
next article High-precision computation of the weak Galerkin methods for the fourth-order problem

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Metadata
Title
Unfitted finite element for optimal control problem of the temperature in composite media with contact resistance
Authors
Qian Zhang
Tengjin Zhao
Zhiyue Zhang
Publication date
13-06-2019
Publisher
Springer US
Published in
Numerical Algorithms / Issue 1/2020
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-019-00750-6

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