A finite element method with grouped smooth constraints

The accurate computation of potential derivatives is a key process in numerical calculation, e.g. finite element method (FEM), of electromagnetic fields. According to the continuity of electromagnetic field, we propose a new FEM formula, in which a high order polynomial interpolating function conquering all nodal potentials in a group of neighboring elements is taken as a smooth constraint to the FEM functional. Compared with the traditional FEM, the new method can considerably improve the field calculation accuracy, and reduce the scale of the FEM stiff matrix. Numerical experiments show that the errors of the computed field vectors are reduced considerably.