As the mesh is refined, the computed solution will approach the true solution. Leaving aside the computational cost associated with a large number of elements, is there any numerical issue related to the solution of a general structural problem (linear or nonlinear, static or dynamic) when the mesh is refined beyond any reasonable amount? In other words, is there any lower limit for the size of the element for a given structural problem? This question would extend to electromagnetic simulations as well. Thanks
There's no absolute limit, but there is a practical limit for a given numerical precision (i.e. 64-bit floating-point). Refining the mesh means adding up a larger and larger number of finer and finer contributions, which does have the potential for numerical instability. There's no hard and fast rule because it depends on the details of the simulation code as well as the model being simulated, but yes, it's possible to go too far. General advice (besides "use common sense") is to refine until the results converge (stop changing very much with further refinement) and then stop.