Superconvergence error analysis of linearized semi-implicit bilinear-constant SAV finite element method for the time-dependent Navier–Stokes equations
Communications in Nonlinear Science and Numerical Simulation(2024)
摘要
In this paper, based on the scalar auxiliary variable (SAV) approach, the superconvergence error analysis is investigated for the time-dependent Navier–Stokes equations. In which, an equivalent system of the Navier–Stokes equations with three variables and a fully-discrete scheme is developed with semi-implicit Euler discretization for the temporal direction and low-order bilinear-constant finite element discretization for the spatial direction, respectively. With the help of the high-precision estimations of the bilinear-constant finite element pair on the rectangular meshes, the superclose error estimates for velocity in H1-norm and pressure in L2-norm are obtained by treating the trilinear term carefully and skillfully. The global superconvergence results are also derived in terms of a simple and efficient interpolation post-processing technique. Finally, some numerical results are provided to demonstrate the correctness of the theoretical analysis.
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关键词
Time-dependent Navier–Stokes equations,Semi-implicit SAV Galerkin scheme,Bilinear-constant finite element discretization,Superclose and superconvergence error estimates
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