Accuracy estimate for magnetic electron lenses computed by first-order FEM

The paper gives a method to estimate the accuracy of potential computed with the first-order FEM in rotationally symmetric magnetic electron lenses. The local estimate of errors in the magnetic flux are computed as a difference between the flux computed in a given mesh and in a denser mesh with twice the number of mesh points in each direction. This quantity allows us to identify critical places in the mesh. In most cases we check only the error of axial flux density to explain the accuracy of determination of optical properties.