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The purpose of this paper is to analyze the accuracy of finite element method simulations for high voltage equipment featuring resistive field grading.

In such simulations, the order of the mesh used and the polynomial order of the ansatz functions are varied while maintaining mesh and simulation parameters. The resulting accuracy of the simulations is analyzed by an error convergence study which shows the relative errors against the number of degrees of freedom the computational time and the memory consumption.

Simulation results of simplified benchmark geometry and applications to large‐scale 3D high voltage equipment are presented herein.

The impact of the order of the mesh and the Ansatz functions are studied for realistic high voltage setups. The paper helps the user of simulation software to choose adequate simulation parameters.

The paper aims at proposing a uniform and demonstrative description of two well‐known and widely used approximations of slowly time‐varying electromagnetic fields, i.e. the electro‐quasistatic and the magneto‐quasistationary approximation to Maxwell's equations.

Under both approximations, the orders of magnitude of the relative errors of the dominant fields are analyzed by using three characteristic time constants. These time constants are determined by considering the material properties, the characteristic length scale and the characteristic time scale.

Limiting curves which show the domains of applicability of the two approximations are retrieved from the estimation of their relative errors. The relation between the domains of validity of the electro‐quasistatic and magneto‐quasistationary approximations was found and depicted in a combined diagram.

The study is restricted to slowly time‐varying electromagnetic fields. Heuristic and local estimates based on local material properties were used for the analysis. Rigorous estimations of the errors (e.g. also considering the field problem's topology) of the magneto‐quasistationary approximation are already known in the literature. A rigorous estimation of the error of the electro‐quasistatic approximation is, therefore, suggested for future research.

The combined diagram showing the domains of validity of both approximations considered here in a uniform way is novel. It gives rise to an intuitive and easily accessible understanding of their applicability.

A combination of both time step adaptivity and spatial mesh adaptivity is presented for transient magneto‐quasistatic fields.

Error controlled time step adaptivity is achieved using an implicit integration scheme and the spatial mesh resolution is adapted in each time step in order to effectively resolve the appearing and disappearing local transient saturation effects and eddy current layers. Two spatial refinement strategies are considered, the red‐green refinement leading to a regular mesh and the red refinement leading to an irregular mesh. Numerical results for 2d nonlinear magneto‐dynamic problems are presented.

An algorithm is proposed which computes the solution of a transient magnetostatic problem given a user prescribed error tolerance for the time stepping and the spatial refinement. The red refinement leading to irregular meshes requires projection techniques in the iterative conjugate gradient solver. However, the algorithm with red‐green refinement turns out to perform faster since the projection is too expensive.

The combination of error controlled time stepping and spatial adaptivity is firstly established in electromagnetic field computation.