Hi Cyrus,

I agree with the response provided by Younes and will expand upon his response slightly.

There is a discretization error in the finite element solution because of the approximation of the actual solution field with element shape functions. As you increase the number of elements in the solution, they provide a more accurate representation of the solution field and the discretization error is reduced.

You can perform a convergence analysis or mesh refinement study by tabulating the result a specific location versus the characteristic element size for solutions from different meshes. You can often fit results from this numerical study to an expression of the type: d(h) = d0 + Ah^p where d is a solution variable (at one specific location) like displacement, h is element size. d0, A, and p are fitting parameters. If you do this, then d0 is an estimate of the exact numerical solution and d(h)-d0 is an estimate of the error associated with that variable for the mesh with an element size of h.

Best, DJ Luscher

Thak you both ,Mr Nouri and Mr Luscher, it was so helpful.You know Ive modeled 9 different dental prosthesis, i choose the seed 0.001 but in some models i get 2 nodes to close and makes me change the seed ,and when i do that the results arent corresponds to others.

FEM results are always mesh dependent. For better results use finer mesh.

I would recommend that you read the paper by: MacNeal & Harder - Standard Problems FE Accuracy. It shows how standard elements fail to produce the analytical solution. 

Please do a mesh independence study initially.

thanks all.

In numerical simulation, depend on the mesh refinement and type of the elements, different results is obtained. The results for a very coarse mesh will differ from an analysis made on the same structure using a denser mesh. Therefore, you need to carry out a sensitivity analysis and convergence study to be sure that the response of model is the same with different mesh size and you will see in finer mesh.