LAUSR

The current paper establishes different axisymmetric and two-dimensional models for an electrostatic, magnetostatic and electromagnetic induction process. Therein, the Maxwell equations are combined in a monolithic solution strategy. A higher order finite element discretization using Galerkin’s method in space as well as in time is developed for the electromagnetic approach. In addition, time integration procedures of the Runge–Kutta family are evolved. Furthermore, the residual error is introduced to open an alternative way for a numerically efficient estimation of the time integration accuracy of the Galerkin time integration method. Runge–Kutta methods are enriched by the embedded error estimate. A family of electrostatic, magnetostatic and electromagneto dynamic boundary and initial boundary value problems with existing analytical solutions are introduced, which will serve as benchmark examples for numerical solution procedures.