I recently came across a term 'hanging nodes' in finite element method while reading about adaptive mesh refinement.

A hanging node is a node, usually on the edge of an element but does not belong to that element. This occurs in non-conformal meshing created during adaptive mesh refinement.

Of course the simplest way to get rid of hanging node is splitting the element in two new element making a vertices at the hanging node. But some other ways should be possible. Please comment below if you know any other way of getting rid of hanging node.