Error estimates of the space–time spectral method for parabolic control problems☆

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Abstract

This work is devoted to investigate the spectral approximation of optimal control of parabolic problems. The space–time method is used to boost high-order accuracy by applying dual Petrov–Galerkin spectral scheme in time and spectral method in space. The optimality conditions are derived, and the a priori error estimates indicate the convergence of the proposed method. Numerical tests confirm the theoretical results, and show the efficiency of the method.

Keywords

Optimal control
Parabolic equations
Space–time spectral method
A priori error estimates

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The first author was supported by the National Natural Science Foundation of China (Grant No. 11601466). The first author and the second author were supported by the Nanhu Scholars Program for Young Scholars of XYNU, and Doctoral Scientific Research Startup Fund of Xinyang Normal University (2016).

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