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论文类型：期刊论文

发表时间：2019-07-30

发表刊物：MATHEMATICAL METHODS IN THE APPLIED SCIENCES

收录刊物：SCIE、EI

卷号：42

期号：11

页面范围：4008-4016

ISSN号：0170-4214

关键字：divergence-free; finite elements; fluid mechanics; quadrilateral; stokes element

摘要：This short note reports a lowest order divergence-free Stokes element on quadrilateral meshes. The velocity space is based on a P-1 spline element over the crisscross partition of a quadrilateral, and the pressure is approximated by piecewise constant. For a given quadrilateral mesh, this element is stable if and only if the well-known Q(1)-P-0 element is also stable. Although this method is a subspace method of Qin-Zhang's P-1-P-0 element, their velocity solutions are precisely equal. Moreover, an explicit basis representation is also provided. These theoretical findings are verified by numerical tests.