L2-Norm Based a Posteriori Error Estimates of Compressible and Nearly-Incompressible Elastic Finite Element Solutions
Round 1
Reviewer 1 Report
Please see the attached PDF for comments.
Comments for author File: 
Comments.pdf
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 2 Report
The author presented in the manuscript the a-posteriori error estimations of finite element solutions based on the recovery of displacement and stress. The paper is well organized, it is recommended the paper be accepted after minor revision. Some suggestions:
-In the Abstract and Conclusions, it is recommended to present some of the main results obtained in the study in quantitative terms.
- Introduction part must be improved. It should contain a critical review of literature, a presentation of the research gap, emphasis on the article's novelty and originality. Hence, the authors are recommended to improve this part. In the current version, the authors have listed plenty of results presented in the literature, more comments about the research gap should be added, especially on page 2.
- Line 225, 4(a) can be only (a), no need to add 4. Similar problems are recommended to be modified.
- Line 8 ‘..edu.sa’, one point should be deleted.
- Some figures seem to be the same as the ones presented in reference [24]. Better to add the citation.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 3 Report
In my opinion authors should clarify/modify the following issues:
#1) Abstract. The first sentence is confusing. Please rewrite it.
#2) Lines 31, 32. Please do not use “the” in “the industrial problems” and “the errors are”. A deep revision of English throughout the paper is needed
#3) Please include in the Introduction section critical remarks about their relation with the topic covered by the paper. An example in which a simple comment of reference #2 is included without remarking the relation with the paper appears in page 1. Line 41, or in line 58 “so-called Zienkiewicz and Zhu (ZZ) recovery technique is presented bv Zienkiewicz and Zhu [6] to…”. In this sentence please correct the typo “by” instead of “bv”.
#4) Line 48. Please be more precise. What is the meaning of “and are simple”?
#5) Line 48. Please use always italics for latin expressions such as “a posteriori”
#6) Line 101. Please use “Gauss point” Instead of “gauss point”
#7) Lie 107. Please avoid sentences such as “are quantified in quantity of error…”
#8) For the sake of clarity, please always use italics for variables such as “u” (line 131) or “a” (line 126). Do the same throughout the manuscript.
#9) Line 144. The variable omega is not defined in equations 8-10.
#10) Line 149 and equation 13. Please use the same subindex for accuracy symbol “allow” or “allowable”.
#11) Line 162. Please include the number of nodes of triangular elements used (linear, quadratic…). In addition, for the sake of clarity, please show the boundary conditions. Show them in Fig. 1. In addition, authors do not explain how meshes are made in all the examples shown. Which software is used?. How the values are obtained?.
#12) Line 168. For the sake of clarity, define terms appearing in line 168.
#13) Line 172. Please do not use a dot for scalar product, it is confusing. Please do the same in equations 20 and 21.
#14) Line 173. Please use “is the Young modulus and the Poisson´s ratio”. In addition, include a remark about if the numerical values are taken from a given material (please show which material) or they are just theoretical values.
#15) Tables 1-5. How FEM error is estimated?. In addition, error values are given as absolute values, is it not? In my opinion, percentage values of the error should be more interesting for the analysis. In addition, in Tables 3 to 5, DOF (degrees of freedom) is not defined (it is defined for table 6 and 7 lately in line 202). Please show how are obtained.
#16) Line 233. Please use a dot instead of “,” before “It”.
#17) Line 237. Words seem to be smaller than the other paragraphs. Please use the same letter size for this sentence.
#18) Line 265. Equations 25 to 27. Do not use a dot for scalar product, please use a blank space instead.
#19) Line 270. The parameters young modulus and Poison ratio are previously defined in line 173. In addition, delete the extra dot in “[. (1-2…..”
#20) In section “4. Discussion “ lines from 298 to 315 are just a summary of previous sections, not a discussion of obtained results. In a similar way, lines from 327 to 335 are again a summary. In my opinion, a deeper discussion of obtained results is needed with a quantitative analysis instead of a qualitatively analysis of the errors obtained (“the error obtained…..is much lower than…..”, line 316 or line 319 “the displacement based recovery technique gives more accurate…… or “….has higher effectivity than….”, line 322). Plots of the analysed variables should be helpful for the discussion.
#21) Reference section must be carefully revised. Some references use the abbreviated journal name (se, refs. 1,2,4, 9, …, 21) and other the full journal name (see, ref. 3, 5,7,…,14,…..).
#22) Ref. 8, 12. The journal name must be in italics.
#23) Something seems to be missed in journal pages of ref. 3. (9-8)
#24) ref. 11. Please delete the extra “()”
#25) Some reference are incomplete (journal number, pages,) for instance, refs. 12, 14, 15,17, 20, 21.
#26) Some references has a blank space between the author initials and others have not. For example, refs. 13 “F.J.” and refs. 25 and 26 “G. C.”. please unify.
# 27) Please use “Díez” instead of “D´iez” and “Ródenas” instead of “ R´odenas” in ref. 13.
#28) please unify the doi. Some are given as “https://....” (see for instance, refs 12, 17,24) and others as “DOI:..” (see for instance, refs. 18, 21) and others are not given (see for instance, refs. 22, 25). Please include the missed doi.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The current version is suitable for publication.
Reviewer 3 Report
