论文标题
发散 - 无scott-弯曲域上的Vogelius元素
Divergence--free Scott--Vogelius elements on curved domains
论文作者
论文摘要
我们在二维中构建和分析了一个等型有限元对，以解决Stokes问题。这对是通过通过Piola变换绘制Scott-Vogelius有限元空间来定义的。速度空间具有与二次拉格朗日有限元空间相同的自由度，因此所提出的空间还原为域内部的Scott-Vogelius对。我们证明，所得的方法以最佳顺序收敛，是无差异的 - 没有压力，并且压力强大。提供了支持理论结果的数值示例。
We construct and analyze an isoparametric finite element pair for the Stokes problem in two dimensions. The pair is defined by mapping the Scott-Vogelius finite element space via a Piola transform. The velocity space has the same degrees of freedom as the quadratic Lagrange finite element space, and therefore the proposed spaces reduce to the Scott-Vogelius pair in the interior of the domain. We prove that the resulting method converges with optimal order, is divergence--free, and is pressure robust. Numerical examples are provided which support the theoretical results.
