变粘性Oseen问题的速度-涡量-压力列式
Velocity-vorticity-pressure formulation for the Oseen problem with variable viscosity
摘要：
我们提出并分析了一种增广的混合有限元法的Osen方程的速度，涡量和压力的非常数粘性和齐次Dirichlet边界条件的速度。弱制定包括最小二乘项所产生的本构方程和不可压缩性条件，我们表明，它满足的Babu \vska -Brezzi理论的假设。重复连续分析的论点，建立了离散问题的稳定性和可解性。该方法适用于速度和压力的任何Stokes inf-super稳定有限元对，而对于涡量，可以使用任何通用的离散空间（任意阶）。先验和后验误差估计来自使用两个特定的家庭的离散子空间。最后，我们提供了一组数值试验，说明该计划的行为，验证理论收敛速度，并显示性能的自适应算法的指导下，残余后验误差估计。
英文摘要：
We propose and analyse an augmented mixed finite element method for the Oseen equations written in terms of velocity, vorticity, and pressure with non-constant viscosity and homogeneous Dirichlet boundary condition for the velocity. The weak formulation includes least-squares terms arising from the constitutive equation and from the incompressibility condition, and we show that it satisfies the hypotheses of the Babu\vska-Brezzi theory. Repeating the arguments of the continuous analysis, the stability and solvability of the discrete problem are established. The method is suited for any Stokes inf-sup stable finite element pair for velocity and pressure, while for vorticity any generic discrete space (of arbitrary order) can be used. A priori and a posteriori error estimates are derived using two specific families of discrete subspaces. Finally, we provide a set of numerical tests illustrating the behaviour of the scheme, verifying the theoretical convergence rates, and showing the performance of the adaptive algorithm guided by residual a posteriori error estimation.
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