ABSTRACT
The finite-element method is based on the following key idea: Since the (Maxwell) equations are formulated for piece-wise continuous functions over space and time, the ultimate goal is to find a valuable approximation of these continuous functions. In other words: the aim is to replace the error-free or exact continuous solution of the equations by an approximate piece-wise continuous functions. The most essential concept in the finite-element method is the element. Mesh creation is an important aspect in finding good approximate solutions. It is evident that if a function is very smooth over a certain region then a few element suffice to capture its values. However, if the function has much variation over a region it is required to use many elements in order to a get a faithful approximation. The finite-element method is very useful for the simulation of scalar-valued fields.
