Element computation

A very significant strength of the finite element method is that it can, to a large extent, be automated. The discretisation of the problem domain, the forming of the element matrices and their combining into global matrices, the solving of the equations and the displaying of the solution, are all tasks which can be adapted for the computer. In this chapter the technique for computing the terms of the element matrices will be described. At the heart of the process is a mapping, which relates the actual element to an element of more regular shape and with axes in a more convenient position. Added to this is a numerical technique for the integration, once the terms of the matrix have been expressed as integrals on the regular shape. Finally, a brief description is given on how the discretisation of the problem domain, the mesh generation, may be automated. Thus the chapter describes: