Electromagnetic equations in the discrete domain
Calculation of electromagnetic fields at low frequencies

The analytical resolution of the formulations proposed above (§ ) is generally impossible, except in the case of systems with simple geometry. Since its solution, which we call "exact", is not accessible, we resort to numerical methods. A discretized model is then obtained, leading to an approximate "discrete" solution. Of the many numerical methods available, we will only discuss the finite element method, which is currently the most widely used for solving low-frequency electromagnetic problems. .

In this section, we recall the weak formulations used to discretize Maxwell's equations. We then present the finite-dimensional functional spaces to which the discretized electromagnetic fields belong. These spaces...