ABSTRACT
The finite element method (FEM) is based on a variational formulation of Maxwell’s equations that involves integral expressions on the computational domain. Unlike, for example the finite-difference method which approximates Maxwell’s equations directly, the FEM leaves Maxwell’s equations completely intact but approximates the solution space in which one tries to find a reasonable approximation to the exact solution. The most common examples of finite elements are triangles and rectangles in 2D and tetrahedrons and cuboids in 3D together with constant, linear, quadratic, and cubic polynomials. These locally defined polynomial spaces have to be pieced together to ensure tangential continuity of the electric and magnetic field across the boundaries of neighbouring patches. A huge contribution of many other authors has added to the field, which makes the FEM today a very flexible, effective, and well-studied method for electrodynamical simulations. A survey of finite element studies with focus on nano-optical applications.
