Vector Finite Element Approach
Many problems in physics and engineering are governed by partial-differential equations. In fact the form of elements finally employed in the present work is equivalent to the conventional one although they are actually constructed from the viewpoint of generalised vector finite elements. The finite element method or finite element analysis, a technique of converting differential equations into algebraic ones, provides a most powerful tool for solving those problems. A matrix equation representing the original problem is then assembled by using Galerkin’s technique whereby the testing space is chosen to be the same as the expansion space, that is, the two finite sets of vector basis functions are chosen to be identical. The concepts and methodology presented can be extended to higher-order vector shape functions, the discussion having been confined to first-order vector shape functions for simplicity. A singularity would arise at any corners of the boundaries or the interfaces between different media.