Removal of spurious solutions in finite element vector boundary-value problems

A strategy for eliminating spurious computational modes in vector FEM (finite element method) boundary-value problems is proposed. It consists of modifying the weak form of the governing vector equation. This is directly related to the penalty term alteration in the eigenvalue context without the need to select a problem-dependent penalty parameter. The main advantage of this approach is that it involves only a trivial change in conventional FEM formulations which can be carried out during element assembly. Thus, it preserves all the attractive features associated with standard scalar bases, including energy balance, explicit enforcement of boundary conditions on normal field components, coupling to exterior solutions (hybrid methods), and validity on meshes composed of the simplest of linear and bilinear elements. Results obtained with this approach are presented.<>