Unconditional Superconvergence Error Estimates of Semi-Implicit Low-Order Conforming Mixed Finite Element Method for Time-Dependent Navier–Stokes Equations

Xiaoling Meng and Huaijun Yang ()
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Xiaoling Meng: School of Mathematics, Zhengzhou University of Aeronautics, Zhengzhou 450046, China
Huaijun Yang: School of Mathematics, Zhengzhou University of Aeronautics, Zhengzhou 450046, China

Mathematics, 2023, vol. 11, issue 8, 1-17

Abstract: In this paper, the unconditional superconvergence error analysis of the semi-implicit Euler scheme with low-order conforming mixed finite element discretization is investigated for time-dependent Navier–Stokes equations. In terms of the high-accuracy error estimates of the low-order finite element pair on the rectangular mesh and the unconditional boundedness of the numerical solution in L ∞ -norm, the superclose error estimates for velocity in H 1 -norm and pressure in L 2 -norm are derived firstly by dealing with the trilinear term carefully and skillfully. Then, the global superconvergence results are obtained with the aid of the interpolation post-processing technique. Finally, some numerical experiments are carried out to support the theoretical findings.

Keywords: Navier–Stokes equations; linearized Euler scheme; low-order conforming MFEM; superconvergence error estimates (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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