ABSTRACT
This chapter presents a short elementary introduction to the theory of distribution particularly for engineers and scientist who have the constraints of basic knowledge and time. The weak formulation, which lies at the heart of our finite element method, simplifies the treatment of complex boundary conditions and eliminates the problems of concentrated loads. The theory of distribution provides an elegant method of derivative for the functions which are not differentiable in the classical sense. Sobolev embedding theorems are important to analyze the continuity of function for higher dimensional domain. Sobolev spaces simplify our problem in the sense that the test function need not belong to the space of infinitely differentiable functions. Monotonic convergence can only be guaranteed for conforming elements, but there are several non-conforming elements in practical use in commercial finite element systems. Non-conforming elements are therefore required to pass the patch test in which a constant strain field is applied to an assembly of arbitrarily oriented elements.
