SYNTHESIS OF VECTOR PARASITES IN FINITE-ELEMENT MAXWELL SOLUTIONS

Closed-form solutions to driven boundary value problems are obtained f or the discrete finite element forms of the double-curl, penalty, and Helmholtz equations, as realized on simple C-degrees bilinear elements . The solutions are expressed as a composite of physical and spurious vector modes, and are qualitatively similar to numerical solutions rep orted on more complex geometries. The findings reveal the critical rol e of discrete boundary conditions in determining the strength of the s purious modes; the overall superiority of the Helmholtz weak form; and the importance of proper boundary conditions for its successful use. In particular, one blend of normal and tangential conditions which app ears well-posed is shown to be inappropriate; and a simple alternative is shown to work well.