  A finite element method using B-splines is presented and compared with a
conventional finite element method of Lagrangian type. The efficiency of both
methods has been investigated at the example of a coupled non-linear system of
Dirac eigenvalue equations and inhomogeneous Klein-Gordon equations which
describe a nuclear system in the framework of relativistic mean field theory.
Although, FEM has been applied with great success in nuclear RMF recently, a
well known problem is the appearance of spurious solutions in the spectra of
the Dirac equation. The question, whether B-splines lead to a reduction of
spurious solutions is analyzed. Numerical expenses, precision and behavior of
convergence are compared for both methods in view of their use in large scale
computation on FEM grids with more dimensions. A B-spline version of the object
oriented C++ code for spherical nuclei has been used for this investigation.
