L. Demkowicz et L. Vardapetyan, MODELING OF ELECTROMAGNETIC ABSORPTION SCATTERING PROBLEMS USING HP-ADAPTIVE FINITE-ELEMENTS/, Computer methods in applied mechanics and engineering, 152(1-2), 1998, pp. 103-124
A model problem for the steady-state form of Maxwell's equations is co
nsidered. The problem is formulated in a weak form using a Lagrange mu
ltiplier, laying down a foundation for a general class of novel hp-ada
ptive FE approximations. A convergence proof for affine elements is pr
esented. The proposed method is illustrated and verified with a series
of 2D experiments including elements with curved boundaries and nonho
mogeneous media.