Comparing 3D finite element formulations modeling scattering from a conducting sphere

Six tetrahedral finite-element varieties are used to model the frequency-domain open-region scattering problem of a ka=2 conducting sphere. A wave-absorbing boundary condition is imposed at kr=3. Linear and quadratic node-based elements display vector parasites, which are less significant in the quadratic element case. Whitney edge elements improve with increasing mesh density, but accuracy is costly due to approximately linear h-convergence. Whitney elements also result in acceptably fast convergence of a biconjugate gradient iterative solver, alone among the elements examined. Novel weighted Whitney elements show some effectiveness and appear free of vector parasites, but are not as cost-effective as Whitney elements. Higher-order tangential elements appear cost-effective, in that accurate solutions may be obtained at low mesh density