Condition numbers for various FEM matrices

A detailed study is presented that examines the inter-relationships between condition numbers of finite element method (FEM) matrices based on various interpolatory and hierarchical tangential vector finite elements (TVFEs). The validity of the generally accepted postulate that interpolatory higher order TVFEs lead to better conditioned matrices than hierarchical higher order TVFEs is found to be questionable. Based on the study, an approach for improving the condition number of FEM matrices resulting from selective field expansion (different order TVFEs combined within the computational domain for effective discretization of the unknown field) is suggested and tested. The improvement comes at the expense of a more complicated formulation and computer code but does not alter accuracy.