As I understand the mesh convergence analysis you should simply decrease the element size in each body by chosen factor and solve the problem again and then if the desired quantities will not change by more than 5% than you can say the rougher mesh is fine enough and your results do not depend on the mesh size. The problem here is that I do not think that there is a standard how to choose the size of the finer mesh. Logically it could be either that your finer element size will be half size compared to rougher one or that total number of elements of the finer mesh increased twice compared to the rougher mesh. The first choice is natural for regular mesh while the other seems to be more appropriate for irregular meshes. However it will always depend on how you gonna defend your mesh convergence analysis in the paper after all.

As I understand the mesh convergence analysis you should simply decrease the element size in each body by chosen factor and solve the problem again and then if the desired quantities will not change by more than 5% than you can say the rougher mesh is fine enough and your results do not depend on the mesh size. The problem here is that I do not think that there is a standard how to choose the size of the finer mesh. Logically it could be either that your finer element size will be half size compared to rougher one or that total number of elements of the finer mesh increased twice compared to the rougher mesh. The first choice is natural for regular mesh while the other seems to be more appropriate for irregular meshes. However it will always depend on how you gonna defend your mesh convergence analysis in the paper after all.

In mesh convergence analysis decrease the element size or inturn you incrase the number of elements. also the deploment of elements depends upon the shape of the object. you go on invreasing element density untill you get solution different is less than 2% when compared to previous solution. this indicates the solution is converged.

you can refer my paper which was published in international journal. i have completly described regarding convergence study

Article Buckling Studies on Laminated Composite Skew Plates

I think in your situation the easiest way is to do adaptive mesh which does automaticly reducing the element size where it is needed.

As Aziz said adaptive technique would be helpful in your case. However, this technique is not applicable for all materials, elements, and analysis depending on the used FE software. So if you cannot use adaptive meshing technique, you supposed to follow Srinivasa's procedure, i.e. reducing your mesh sizes until achieving a meaningful convergence in obtained results. This technique is a kind of try and error so it would be time consuming if you run a full analysis for each mesh size. In many cases you can consider only part of your analysis in this step. For example if your loading duration is 10s, use only half of that to find the best mesh size.

Adopting a reasonable mesh size depends on many factors including nature of analysis, model geometry, required level of accuracy, material behavior, etc.

Thank you all for helping on this. I know that these kind of analyses are done by reducing the element sizes of all bodies in a model half during each subsequent mesh steps. However, the thing I wondered was that above mentioned rule is also valid when using a mixture of different element shapes, (tetrahedral and hexahedral) or there exists any other way? The reason I asked this question was that I got an objection in one of my papers I submitted. One of reviewers pointed out that decreasing element size thing might not be good idea if you use a mixture of elements.

By the way, I use ADINA for finite element simulations and as far as I know adaptive mesh technique is not used in this software. Please tell me if I am wrong.

The mesh convergence study is based on two types of refinements known as h- and p- refinement. In h-refinement the element size is reduced ( number of elements increased), while in p-refinement, the order of interpolation functions of elements is increased such as using higher order quadratic elements instead of using first order linear elements. The h-refinement can be used in problems with simple geometries whereas the p-refinement can be used more for complex geometries involving holes and curvatures. However, combination of both will result in better solution. In my view, that's what the reviewers has asked for.

Your reviever is probably wrong. Decreasing the size of elements works fine even for mixed mesh. The exceptions are usually not connected with topology of elements, but with geometry. For sharp, loaded corners in some specific situations refining the mesh will not give you better results. So review carefully your geometry, if there is no such geometrical stress concentrators, especially in max stress areas.

The choice of decreasing size or number of element by factor 2 is not a main problem. It depends on power of your computer. At least 3 densities should be checked.

By the way, the approach of Srinivasa Chikkol with 2% difference is a little obsolete. Nowadays, the better results can be obtained with the use of Roache convergence criterion, where on the basis of results for a few mesh densities, you can predict the exact solution.

More about the Roache criterion in:

http://www.grc.nasa.gov/WWW/wind/valid/tutorial/spatconv.html

http://blog.pointwise.com/2012/07/05/accuracy-convergence-and-mesh-quality/

http://www.dynamore.de/de/download/papers/forum08/dokumente/I-I-03.pdf

and its references.

According to answer of Himayat Ullah,

changing order of element from linear to parabolic (II order) cannot be treated as mesh convergence study. It's rather selecting of proper elements for analysis.

In fact, p-refinement is used with special kind of finite element, in which the order of shape function can be changed. This kind of element in modern FEM codes are depreciated, and this technique is rather not used.

Manual remeshing with twice smaller global element size IS a requested mesh convergence study. This action shouldn't be treated as h-refinement, because both p- and h- refinements are intented to be done automatically and locally on the basis of excessive stress gradients. H-refinement is in fact almost the same as adaptive meshing (not allowed in Adina),

By the way, in case of analysis with steel and bone in contact, I were worried rather by relative mesh density of both meshes, and contact stiffness definition, because of significant difference of stiffness of both materials.

Both types of h- and p-refinements are treated as mesh refinements for mesh convergence. Rather, there is another type called r-refinement in which 'r 'means rearrange, that is existing nodes are moved without changing the number of elements or the number of DOFs. These refinements are usually used in combination. According to Robert D Cook, for problems containing singularities, such as reentrant corners or cracks, p-refinement converges much faster than h-refinement.

In my view, Artur Iluk is confusing the automatic adaptive remeshing with mesh convergence. However, adaptive remeshing is not a capability of most FE codes. In many cases, manual mesh refinements are required. Further details on the topic can be read from " Section 5.15 Convergence with mesh refinement" of " Finite element modeling for stress analysis" by Robert D. Cook.

OK, maybe its only difference in used terminology. In my view, the term mesh convergence study is usually applied to decreasing element size globally, while p-, h-, r-refinement and adaptive remeshing are used getting better results locally, where stress gradients are to high.

I wonder, how Mr Cook could write, that "p-refinement converges much faster than h-refinement" for stress in cracks (tip of crack, as I understood). This is one of situations, when simulation will newer converge, because stress values goes to the infinity. It this case, only stress intensity factor can by calculated.

Theoretically, the stress values go to the infinity but practically there exists some meaningful stress value at the crack tips. That is why the Linear Elastic fracture mechanics (LEFM) and linear elasricity theories are limited in analysing the crack gorwth as there exists some plastic zone ahead of the crack tip known as cohesive zone introduced by Dugdala and Barrenblatt. In such situations if p-refeinement is used, it converges faster than the the h-refinement. Further LEFM based simulations also need huge mesh refinements at the crack tips,

Hi every one! I have a question related to this subject. I have a turbulent flow for a channel. But for a first approximation I modeled it in laminar condition. the results had an approximate error about 30-35%. Can I perform the mesh study on the laminar case or It has to be in turbulent case? Thanks for help.

Good question.. Please share me the best answer might you trust...

Regards…