Two-Level Method Based on Finite Element and Crank--Nicolson Extrapolation for the Time-Dependent Navier--Stokes Equations
作者： Yinnian He
DOI: 10.1137/S0036142901385659
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摘要: A fully discrete two-level finite element method (the method) is presented for solving the two-dimensional time-dependent Navier--Stokes problem. The requires a Crank--Nicolson extrapolation solution $(u_{H,\tau_0},p_{H,\tau_0})$ on spatial-time coarse grid $J_{H,\tau_0}$ and backward Euler $(u^{h,\tau},p^{h,\tau})$ space-time fine $J_{h,\tau}$. error estimates of optimal order are derived. Compared with standard one-level based $J_{h,\tau}$, same as in H1-norm velocity L2-norm pressure. However, involves much less work than method.
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