The general textbooks of finite element theory introduce these theoretical knowledge in detail, including node freedom, displacement function, shape function, various matrices and so on. Knowing this, your question can be answered clearly.

In addition, the elements in the finite element theory are somewhat different from those in the program, and the elements in the program may be the combination of several elements in the finite element theory. For example, a shell element is a combination of a plate element and a plane element.