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Indexed by:Journal Papers

Date of Publication:2019-07-30

Journal:MATHEMATICAL METHODS IN THE APPLIED SCIENCES

Included Journals:SCIE、EI

Volume:42

Issue:11

Page Number:4008-4016

ISSN No.:0170-4214

Key Words:divergence-free; finite elements; fluid mechanics; quadrilateral; stokes element

Abstract: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.