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Hybridizable discontinuous Galerkin reduced order model for the variable coefficient advection equation

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Abstract

In this paper, a hybridizable discontinuous Galerkin (HDG) model order reduction technique is proposed to solve the variable coefficient advection equation. In order to obtain a high precision original full order model (FOM), the HDG and diagonally implicit Runge–Kutta (DIRK) methods are used for space and time discretization, respectively. The obtained FOM can achieve higher order accuracy in both space and time. Then, we introduce POD method and Galerkin projection to construct the reduced order model (ROM). Compared with the FOM, the proposed ROM can maintain the same higher order accuracy and greatly reduce the computational cost. Finally, some numerical results are illustrated to confirm the validity and higher order accuracy of the proposed reduced order HDG method.

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Authors and Affiliations

  1. College of Mathematics and Statistic, Guangxi Normal University, Guilin, 541006, People’s Republic of China

    Jing Wang, Ying Ye, Danchen Zhu & Lingzhi Qian

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  1. Jing Wang
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  2. Ying Ye
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  3. Danchen Zhu
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  4. Lingzhi Qian
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Correspondence to Lingzhi Qian.

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This work is part supported by the NSF of China (No. 11861054), the Natural science Foundation of Guangxi (No. 2020GXNSFAA297223), the NSF of China (Nos. U19A2079, 11671345 and 11771348).

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Wang, J., Ye, Y., Zhu, D. et al. Hybridizable discontinuous Galerkin reduced order model for the variable coefficient advection equation. Comp. Appl. Math. 42, 263 (2023). https://doi.org/10.1007/s40314-023-02396-6

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  • DOI: https://doi.org/10.1007/s40314-023-02396-6

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