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Fully Discrete Discontinuous Galerkin Numerical Scheme with Second-Order Temporal Accuracy for the Hydrodynamically Coupled Lipid Vesicle Model

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Abstract

In this paper, for the highly nonlinear hydrodynamically coupled elastic bending energy model of vesicle membranes, based on the discontinuous Galerkin (DG) method for spatial discretization, a linear, decoupled, and second-order time-accurate numerical scheme is constructed. The scheme combines several efficient approaches, including the scalar auxiliary variable (SAV) method for the linearization of the nonlinear energy potential, the implicit-explicit (IMEX) discretization method for dealing with the nonlinear coupling terms, and the projection method for the Navier–Stokes equations. We also rigorously establish the energy stability and optimal error estimates, and also carry out several numerical examples to demonstrate the accuracy, stability, and efficiency of the proposed fully discrete DG scheme, numerically.

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Acknowledgements

The authors are grateful to the reviewers for the constructive comments and valuable suggestions which have improved the paper. The work of G. Zou was partially supported by China Postdoctoral Science Foundation (2019M662476), and the Key Scientific Research Projects of Colleges and Universities in Henan Province, China (23A110006). The work of X. Yang was partially supported by National Science Foundation of USA with Grant Number DMS-2012490.

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  1. School of Mathematics and Statistics, Henan Engineering Research Center for Artificial Intelligence Theory and Algorithms, Henan Key Laboratory of Earth System Observation and Modeling, Henan University, Kaifeng, 475004, People’s Republic of China

    Guang-an Zou & Zhaohua Li

  2. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA

    Xiaofeng Yang

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  1. Guang-an Zou
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  2. Zhaohua Li
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Correspondence to Xiaofeng Yang.

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Zou, Ga., Li, Z. & Yang, X. Fully Discrete Discontinuous Galerkin Numerical Scheme with Second-Order Temporal Accuracy for the Hydrodynamically Coupled Lipid Vesicle Model. J Sci Comput 95, 5 (2023). https://doi.org/10.1007/s10915-023-02129-1

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