CST mesh problem with small gaps in structures

Currently I am simulating a structure with very small gaps in it. Do I need to set the mesh to cover all the small gaps in my structure? If the mesh cell is larger than the gaps in my structure, can I get the correct result? (The thing is I expect current flows through the gaps to make a continuous current flow in the structure and big mesh cell gives me a good result as I expected, but when I make dense mesh to cover the gaps, I can not get the good result. Is that because in reality, my guess about the current flow through the small gap is impossible?)