Second order corrections to the finite volume upwind scheme for the 2D Maxwell equations

Abstract

When computing solutions to Maxwell equations with finite volumes methods one often faces mesh dependent structures. We describe a way to add second order corrections to the finite volume upwind scheme for the 2D Maxwell equations that are designed to overcome this difficulty. This is done by using exact solutions to the wave equation for each component of the electromagnetic field. We illustrate the method with numerical results on simple test cases.