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Unconditionally Optimal Error Analysis of a Linear Euler FEM Scheme for the Navier–Stokes Equations with Mass Diffusion

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Abstract

In this paper, a linear and decoupled Euler finite element scheme is proposed for solving the 3D incompressible Navier–Stokes equations with mass diffusion numerically by the mini element for the velocity equation and the \(P_2\) conforming element for the density equation. When the time step size \(\tau \) and the mesh size h both are sufficiently small, the proposed FEM algorithm is unconditionally stable at the full discrete level, which is a key issue in designing the efficient algorithm for the multi-physical field problem. Furthermore, optimal temporal-spatial error estimates are presented for the velocity in \(\mathbf{L} ^2\)-norm and the density in \(H^1\)-norm without any constraint of \(\tau \) and h by using the technique of error splitting.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (No. 11771337) and Natural Science Foundation of Zhejiang Province (No. LY18A010021).

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  1. College of Mathematics and Physics, Wenzhou University, Wenzhou, China

    Yuan Li & Rong An

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  1. Yuan Li
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  2. Rong An
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Correspondence to Rong An.

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Li, Y., An, R. Unconditionally Optimal Error Analysis of a Linear Euler FEM Scheme for the Navier–Stokes Equations with Mass Diffusion. J Sci Comput 90, 47 (2022). https://doi.org/10.1007/s10915-021-01730-6

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  • DOI: https://doi.org/10.1007/s10915-021-01730-6

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