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A new fully-decoupled energy-stable BDF2-FEM scheme for the electro-hydrodynamic equations

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  • Li, Mengmeng
  • Zou, Guang-an
  • Wang, Bo

Abstract

In this work, we develop a new linear, second-order accurate, fully-decoupled and unconditionally energy stable finite element method (FEM) for the electro-hydrodynamic system, which describes the charge transport in dielectric liquids. The fully-decoupled scheme is realized by two-step backward differentiation formula (BDF2) method, the stabilizing strategy, implicit-explicit (IMEX) scheme and rotational pressure-projection method. The main feature of this scheme is to add a stabilization term artificially in the conservation of charge density equation, which allows for the explicit treatment of the coupled nonlinear terms, resulting in the decoupling of computations for the velocity field and electric field. A further innovation is the pressure-correction method for the Navier–Stokes system, which achieves the decoupling of the velocity field and pressure. In addition, we exactly prove the unique solvability, unconditional energy stability and provide convergent analysis for the proposed scheme. Finally, several numerical examples are performed to test and verify the theoretical results of the numerical scheme.

Suggested Citation

  • Li, Mengmeng & Zou, Guang-an & Wang, Bo, 2026. "A new fully-decoupled energy-stable BDF2-FEM scheme for the electro-hydrodynamic equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 239(C), pages 172-191.
    • Handle: RePEc:eee:matcom:v:239:y:2026:i:c:p:172-191
    DOI: 10.1016/j.matcom.2025.05.007
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    References listed on IDEAS

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    1. He, Dongdong & Pan, Kejia, 2016. "An energy preserving finite difference scheme for the Poisson–Nernst–Planck system," Applied Mathematics and Computation, Elsevier, vol. 287, pages 214-223.
    2. Yong Zhou & Jishan Fan, 2012. "Uniqueness of Weak Solutions to an Electrohydrodynamics Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Yong Zhou & Jishan Fan, 2012. "Uniqueness of Weak Solutions to an Electrohydrodynamics Model," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-14, May.
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