Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2018-08-15

Journal: COMPUTERS & MATHEMATICS WITH APPLICATIONS

Included Journals: SCIE

Volume: 76

Issue: 4

Page Number: 877-892

ISSN: 0898-1221

Key Words: Nonconforming finite element; Polynomial; Quadrilateral meshes; Uniform convergence; Discrete de Rham complex

Abstract: This work provides a new mixed finite element method for the Brinkman problem over arbitrary convex quadrilateral meshes. The velocity is approximated by piecewise polynomial element space which is H(div)-nonconforming, and the pressure is approximated by piecewise constant. We give the convergence analysis of our element, and especially show the robustness with respect to the Darcy limit. Moreover, via a discrete de Rham complex, a higher-order approximation error term is obtained for incompressible flow. Numerical examples verify our theoretical findings. (C) 2018 Elsevier Ltd. All rights reserved.