Energy-norm-based and goal-oriented automatic hp adaptivity for electromagnetics: application to waveguide discontinuities Articles uri icon

publication date

  • December 2008

start page

  • 3039

end page

  • 3049


  • 12


  • 56

International Standard Serial Number (ISSN)

  • 0018-9480

Electronic International Standard Serial Number (EISSN)

  • 1557-9670


  • The finite-element method (FEM) enables the use of "adapted" meshes. The simultaneous combination of h (local variations in element size) and p (local variations in the polynomial order of approximation) refinements, i.e., hp-adaptivity, is the most powerful and flexible type of adaptivity. In this paper, two versions of a fully automatic hp-adaptive FEM for electromagnetics are presented. The first version is based on minimizing the energy-norm of the error. The second, namely the goal oriented strategy, is based on minimizing the error of a given (user-prescribed) quantity of interest. The adaptive strategy delivers exponential convergence rates for the error, even in the presence of singularities. The hp adaptivity is presented in the context of 2-D analysis of H-plane rectangular waveguide discontinuities. Stabilized variational formulations and H(curl) FEM discretizations in terms of quadrilaterals of variable order of approximation supporting anisotropy and hanging nodes are used. Comparison of energy-norm and goal-oriented hp-adaptive strategies in the context of waveguiding problems is provided. Specifically, the scattering parameters of the discontinuity are used as goal.