A stabilized Crouzeix‐Raviart element method for coupling stokes and darcy‐forchheimer flows. Issue 4 (31st March 2017)

• Record Type: Journal Article
• Authors: Zhang, Jingyuan; Rui, Hongxing
• Is Part Of: Numerical methods for partial differential equations. Volume 33:Issue 4(2017:Jul.)
• Page Start: 1070
• Page End: 1094
• Publication Date: 2017-03-31
• Subjects: coupled Stokes and Darcy‐Forchheimer flows -- Crouzeix‐Raviart element -- error estimates -- stabilized method; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22129
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : In this article, we present a stabilized mixed finite element method for solving the coupled Stokes and Darcy‐Forchheimer flows problem. The approach utilizes the same nonconforming Crouzeix‐Raviart element and piecewise constant on the entire domain for the velocity and pressure respectively. We derive a discrete inf‐sup condition and establish the existence and uniqueness of the problem. Optimal‐order error estimates are obtained based on the monotonicity owned by Forchheimer term. Finally, numerical examples are presented to verify the theoretical results. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1070–1094, 2017