论文标题
后验误差分析和适应性，用于Navier-Stokes方程的VEM离散化
A posteriori error analysis and adaptivity for a VEM discretization of the Navier-Stokes equations
论文作者
论文摘要
我们考虑了2016年由BeirãoDaVeiga，Lovadina和Vacca引入的虚拟元素方法（VEM），用于稳定，不可压缩的Navier-Stokes方程的数值解决方案；该方法具有任意订单$ k \ geq 2 $，并保证无差异速度。对于这种离散化，我们开发了一个基于残差的后验误差估计器，该估计量是VEM分析中标准术语（残留项，数据振荡和VEM稳定）的组合，以及其他一些术语，由非线性对流术语的VEM离散化源自。我们表明，速度和压力误差的线性组合由估计器的倍数（可靠性）限制。我们还建立了一些效率结果，涉及误差的下限。一些数值测试说明了估计量及其组件的性能，同时均匀地完善网格，从而产生预期的衰减速率。最后，我们将自适应网状精炼策略应用于计算通道内方缸围绕平方缸的计算。
We consider the Virtual Element method (VEM) introduced by Beirão da Veiga, Lovadina and Vacca in 2016 for the numerical solution of the steady, incompressible Navier-Stokes equations; the method has arbitrary order $k \geq 2$ and guarantees divergence-free velocities. For such discretization, we develop a residual-based a posteriori error estimator, which is a combination of standard terms in VEM analysis (residual terms, data oscillation, and VEM stabilization), plus some other terms originated by the VEM discretization of the nonlinear convective term. We show that a linear combination of the velocity and pressure errors is upper-bounded by a multiple of the estimator (reliability). We also establish some efficiency results, involving lower bounds of the error. Some numerical tests illustrate the performance of the estimator and of its components while refining the mesh uniformly, yielding the expected decay rate. At last, we apply an adaptive mesh refinement strategy to the computation of the low-Reynolds flow around a square cylinder inside a channel.
