J. Dolbeault, M.J. Esteban, E. Sere A variational method for relativistic computations in atomic and molecular physics. (3618K, Postscript) ABSTRACT. This paper is devoted to the numerical computation of energy levels of Dirac operators with applications in atomic and molecular physics. Our approach is based at a theoretical level on a rigourous variational method. This provides a numerical method which is free of the numerical drawbacks which are often present in discretized relativistic approaches. It is moreover independent of the geometry and monotone: eigenvalues are approximated from above. We illustrate our numerical approach by the computation of the ground state in atomic and diatomic configurations using B-splines.