Numerical Analysis and Comparison of Four Stabilized Finite Element Methods for the Steady Micropolar Equations
Round 1
Reviewer 1 Report
Four different stabilised FEM were presented to solve the micropolar Navier-Stokes equations (MNSE). A priori properties, existence, uniqueness, stability and error estimation based on FEM approximation. Low order FEM pairs were tested using FreeFem++ for penalty, regular, multiscale enrichment, and local Gauss integration methods.
Issues:
1. The author should comment on which lower order pairs may satisfy the LBB conditions for micropolar equations, maybe P1-P0-P1? and compared their results with local Gauss integrals.
2. Could you author comment more on why multiscale method will NOT work for lower order method violating the LBB conditions, as shown in Figure 4. In Ref. Yang, L., Badia, S., & Codina, R. (2016). Computational mechanics, 58(6), 1051-1069 shows a good pressure distribution using stabilised FEM with lower order pairs.
Author Response
Please see the attachment.
Author Response File: 
Author Response.docx
Reviewer 2 Report
Attached is a file
Comments for author File: 
Comments.pdf
Author Response
Thank you very much for your review and pertinent comments.
