A Divergence Free Weak Virtual Element Method for the Stokes Problem on Polytopal Meshes
A Divergence Free Weak Virtual Element Method for the Stokes Problem on Polytopal Meshes
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DOI：
10.1007/s10915-018-0796-5
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发表时间：
2018-08
影响因子：
2.5
通讯作者：
Long Chen;Feng Wang
中科院分区：
文献类型：
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作者：
Long Chen;Feng Wang
提出并分析了求解Stokes问题的几种多边形网格上的虚元方法。压力用不连续多项式近似，而速度用H（div）虚拟单元离散，在单元边界上增加一些切向多项式。使用相应的自由度计算速度的弱对称梯度。该方法的主要特点是它完全保持了发散自由约束，因此速度的误差估计不显式地依赖于压力。
Some virtual element methods on polytopal meshes for the Stokes problem are proposed and analyzed. The pressure is approximated by discontinuous polynomials, while the velocity is discretized by H(div) virtual elements enriched with some tangential polynomials on the element boundaries. A weak symmetric gradient of the velocity is computed using the corresponding degree of freedoms. The main feature of the method is that it exactly preserves the divergence free constraint, and therefore the error estimates for the velocity does not explicitly depend on the pressure.