What does this research mean for the field?

The new Crank–Nicolson mixed covolume method provides a priori error estimates for the control variable, state, and costate variables in parabolic optimal control problems. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

This research aims to establish a new method for solving parabolic optimal control problems using the Crank–Nicolson scheme.

March 2, 2026

A Priori Estimate of Crank–Nicolson Mixed Covolume Method for Parabolic Optimal Control Problems

Key Points

This research aims to establish a new method for solving parabolic optimal control problems using the Crank–Nicolson scheme.
Introduced a mixed covolume method with the Crank–Nicolson scheme for temporal discretization.
Utilized the lowest order Raviart–Thomas element for approximating state and costate variables.
Applied piecewise constant functions for control variable approximation.
Derived priori error estimates for the control variable, state, and costate variables.
Demonstrated improved accuracy through the proposed method.

Abstract

In this paper, we will give a new Crank–Nicolson mixed covolume method for parabolic optimal control problems. The state and costate variables are approximated by the lowest order Raviart–Thomas element and the control variable is approximated by piecewise constant function, while Crank–Nicolson scheme is ultilized for temporal discretization. We derive the priori error estimates for the control variable, the state and the costate variables.

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Cite This Study

Changling Xu (Mon,) studied this question.

synapsesocial.com/papers/69a52d9af1e85e5c73bf0898 https://doi.org/https://doi.org/10.1134/s1995423925700065

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