It is a good practice to perform a mesh convergence study for each new FEA model. Such a check is done by increasing the global or, more commonly, local mesh density by a given factor (e.g. 2 times) and checking the difference in results (mainly maximum stress and displacement) with respect to the previous run. This should be repeated until the difference is negligible (below 5%). It is advised to create a graph showing e.g. maximum stress at a critical location vs mesh density. This way it is easier to notice when the results start to converge.
In some cases, it may happen that the maximum stress will be growing indefinitely regardless of how dense the mesh will be. Such a non-physical effect is known as stress singularity. It may occur due to the following reasons:
concentrated forces
boundary conditions applied to points
sharp corners
contact occurring at a corner
Typical ways of dealing with stress singularities are:
applying loads and boundary conditions to small areas instead of points
adding fillets to sharp corners
including plasticity in material behavior
ignoring singularities and reading stresses away from them if possible
