This is not completely illogical. The discrete solutions computed by a convergent method should all tend to the same limit as h (mesh size) --> 0, but for finite non zero values of h and different meshes it is very common that even very different results are obtained, especially if one is comparing meshes that are not completely homogeneous and are refined in a different way in different portions of the domain. The first step to check the correctness of what you are doing would be to take a series of meshes built each as a refinement of the previous one, so that h decreases each time by approximately a factor 2, and estimate the convergence rate of your approximation. If it does not correspond to the theoretical value, then you definitely have either an implementation error or you are studying a problem in which the convergence theory does not apply (for example because the solution is not regular), so depending on the case you either try to correct the code or rather to use a different benchmark.

This is not completely illogical. The discrete solutions computed by a convergent method should all tend to the same limit as h (mesh size) --> 0, but for finite non zero values of h and different meshes it is very common that even very different results are obtained, especially if one is comparing meshes that are not completely homogeneous and are refined in a different way in different portions of the domain. The first step to check the correctness of what you are doing would be to take a series of meshes built each as a refinement of the previous one, so that h decreases each time by approximately a factor 2, and estimate the convergence rate of your approximation. If it does not correspond to the theoretical value, then you definitely have either an implementation error or you are studying a problem in which the convergence theory does not apply (for example because the solution is not regular), so depending on the case you either try to correct the code or rather to use a different benchmark.

It can happen.

To help in answering your question, please provide more details regarding the problem you are trying to solve: PDE, formulation, domain size, boundary conditions, material properties, FE mesh, and the matrix solver (direct/iterative).

It is quite often and that is why mesh independency is required for numerical works. It depends on how intense the gradient of variables are, so the mesh size needs to be refined. It can also depend on whether the correlations or the used properties are local or average values in some works, but it mainly goes back to the gradient of the properties in the field. For eg, to capture a shock wave accurately, fine mesh resolution is needed at least locally since the properties changes sharply.

Hi,

For mesh Size dependency if everything is right,

1. In case you have "Stress singularity point", Stress will diverge as mesh gets denser. Generally in sharp corner (90 deg) along fixed end boundary cause this problem.

2. If the element gets Distorted, solution should vary.

3. If you use isoparametric formulation, as the shape function is defined for Master element, if the Slave element is distorted too much, the mapped shape function may not be able to represent the Solution for the Geometry as expected.

4. Round off error by computer: May happen for extremely dense mesh!

If any mistake has to be checked,

1. See if you do meshing properly. If you get negative jacobian for integration, the situation is not admissible and you need to change meshing.

2. Look if you define and multiply the Jacobian and Weight properly.

3. Check if you determine the Equivalent nodal forces properly.

Thank you all for your answers.

In fact, I thought that I was wrong at the beginning because when I took a large mesh step I found a very distant solution of the exact solution, but when I refined the mesh and the mesh step tended to 0 my solution tended to the exact Solution.

Thank you once again.