Release Time:2019-11-04  Hits:

Indexed by: Journal Papers

Date of Publication: 2019-07-30

Journal: MATHEMATICAL METHODS IN THE APPLIED SCIENCES

Included Journals: EI、SCIE

Volume: 42

Issue: 11

Page Number: 4008-4016

ISSN: 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.