An analysis of the electromagnetic field based on adaptive finite element is presented in this paper. The performance of the adaptive algorithms, based on an element-element h-refinement technique, is assessed. The features of the refinement indictors, adaptation criteria and error estimation parameters are discussed. The strategy of the adaptive mesh refinement method applied to the eigenvalue problem is studied to improve the accuracy of the eigenvector. Numerical results for pill-box cavity and disc-loaded structure are shown.