Radial Point Interpolation-Based Error Recovery Estimates for Finite Element Solutions of Incompressible Elastic Problems

Round 1

Reviewer 1 Report

Please see suggested corrections in the attached document.

 

Comments for author File: Comments.pdf

Author Response

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Reviewer 2 Report

 The manuscript describes an error recovery method based on radial point interpolation (RPI) in finite element analysis. This approach exhibited good error convergence. The study is well investigated and presented. It can be accepted.

Author Response

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Reviewer 3 Report

The manuscript "Radial Point Interpolation Based Error Recovery Estimates for Finite Element Solutions of Incompressible Elastic Problems" is very interesting, original and new. In this manuscript, the reliability and effectiveness of RPI based error recovery approaches is assessed by 402 adaptive analysis of incompressibility elastic problem including problem with singular- 403 ity. My recommendation is accept as is.

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Reviewer 4 Report

Comments and Suggestions for Authors

Authors have submitted the results of “Radial Point Interpolation Based Error Recovery Estimates for Finite Element Solutions of Incompressible Elastic Problems”. Overall, the research investigation was carried out in considerable detail; the depth of the contents is sufficient and well written. Moderate changes in English are recommended. The suggested revision parts in detail for this version are as follows.

1)      In the introduction part, needs improvement, to be explored more, every cited paper must be discussed accordingly instead of giving a very short description as in line 46 reference no. 4. Therefore, every paper must be explained what their outcomes were.

2)      The introduction part needs improvement, with more published work.

3)      Equation 1, 2 needs to be revised according to reference 23.

4)      Equation 15 needs to be revised according to reference 25.

5)      Line 141, the coefficients a_i and b_j are interpolation constants, according to reference 25.

6)      Line 141, m is the number of polynomial basis functions.

7)      Equations 34, 35, 36, 37, 38 needs to be revised according to reference 28.

8)      The references mentioned need to be reviewed

9)      Moderate English changes required.

Author Response

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Reviewer 5 Report

I consider this research to be very well documented , it is presented in a professional manner. All the citations are relevant to the paper's context. It is to be taken into consideration to cite another paper that deal within a similar subject: Mathematical Approach in Complex Surfaces Toolpaths. Florin Popister, Daniela Popescu, Ancuta Păcurar,  Răzvan Păcurar. Mathematics 2021, 9, 1360. https://doi.org/10.3390/math9121360

Publish as it is.

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Reviewer 6 Report

The present work carried out the mesh free RPI based error recovery for incompressible elastic problems, but there is no new formulation, and the error recovery method and meshfree method of RPI are existing as well. The Radial Basis Functions shape parameters has significant effect on the displacement and stress results, so their effect on the analysis error should be investigated as well.

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Reviewer 7 Report

 

This work presents an implementation of the mesh free radial point interpolation (RPI) based error recovery for finite element analysis of incompressible elastic problems. The displacement-pressure based mixed approach is employed in finite element formulation. In the last decades, the interest on this topic has increased and several works have been published considering this topic. In general, the paper is well-written, and the bibliography review is appropriate for the topic. However, there are important points to be considered:

The actual increment to the literature should be clearly state in the last paragraph of section 1.

There is a mistake about the section numbers, there are two sections 4 and two sections 5. In general, the layout of the work could be improved.

Tables 1-8 are the crucial part of the present work; they should be better discussed in section “Applications to Benchmark Examples” or in section “Discussion”.

Probably, a third (and well explored) example could emphasize the capabilities of the present formulation and give more support to the presented conclusions.

In the flow chart presented at Fig 11 is written: “incomressible” instead of incompressible.

 

 

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Round 2

Reviewer 6 Report

This manuscript can be published in the present form.