论文标题
Stokes特征值问题的VEM近似：先验和后验分析
VEM approximation for the Stokes eigenvalue problem: a priori and a posteriori error analysis
论文作者
论文摘要
本文提出了一种稳定的稳定差异虚拟元素方法和先验性的相关性，并进行了后验误差分析，以一次镜头近似Stokes Spectral问题的特征值和特征性。对于先验分析，我们利用溶液操作员的紧凑性证明特征功能的收敛和特征值的双层收敛性。此外，我们还提出了一个残留类型的后验估计器，我们证明这是可靠和有效的，以执行自适应改进，以允许为非平滑本征函数恢复最佳的收敛顺序。一组代表性的数值示例研究了这样的理论结果。
The present paper proposes an inf-sup stable divergence free virtual element method and associated a priori, and a posteriori error analysis to approximate the eigenvalues and eigenfunctions of the Stokes spectral problem in one shot. For the a priori analysis, we take advantage of the compactness of the solution operator to prove convergence of the eigenfunctions and double order convergence of eigenvalues. Additionally we also propose an a posteriori estimator of residual type, which we prove is reliable and efficient, in order to perform adaptive refinements that allow to recover the optimal order of convergence for non smooth eigenfunctions. A set of representative numerical examples investigates such theoretical results.
