论文标题
p-和hp-虚拟元素的stokes问题
p- and hp- virtual elements for the Stokes problem
论文作者
论文摘要
我们分析了多边形域上的stokes问题的虚拟元素方法（VEM）的p和hp versions。分析的关键工具是速度类似泊松和类似于泊松的VE空间之间存在生物。这使我们能够将Stokes的标准VEM重新解释为VEM，在该VEM中，在类似泊松的VE空间中寻求测试和试验离散速度。这个事实的好处是，我们从[7]中继承了对VE空间中最佳插值的明确分析，以及根据该方法的准确性程度明确的稳定估计值。我们证明了HP-VEM的指数融合，用于具有常规右侧的Stokes问题。我们用该方法的p和HP反元素的数值测试证实了理论估计值。
We analyse the p- and hp-versions of the virtual element method (VEM) for the the Stokes problem on a polygonal domain. The key tool in the analysis is the existence of a bijection between Poisson-like and Stokes-like VE spaces for the velocities. This allows us to re-interpret the standard VEM for Stokes as a VEM, where the test and trial discrete velocities are sought in Poisson-like VE spaces. The upside of this fact is that we inherit from [7] an explicit analysis of best interpolation results in VE spaces, as well as stabilization estimates that are explicit in terms of the degree of accuracy of the method. We prove exponential convergence of the hp-VEM for Stokes problems with regular right-hand sides. We corroborate the theoretical estimates with numerical tests for both the p- and hp-versions of the method.
