Abstract:We will present a family of divergence-free finite elements on 2D and 3D rectangular grids, their bases, computation, and advances over the traditional mixed finite elements. The divergence-free finite element is a type of mixed finite elements where the discrete pressure space is exactly the divergence of the discrete velocity space in incompressible fluid computation. Thus the divergence-free finite element solution is mass conservative pointwise, and also the pressure solution would be computed as a byproduct. An application of the element to Maxwell equation will be shown.