The pollution effect and novel methods to reduce its influence in the mid-frequency range

The classical Galerkin formulation is nearly ubiquitous in production-scale finite element codes. The formulation uses effectively the same space of polynomials for both the solution (trial) and weighting (test) functions. Further, the standard h refinement method of decreasing element size to achieve convergence is equally universal, typically involving only linear and second order polynomial elements. For geometries that are several wavelengths in size the above methodology is sufficient for accurate predictions. However, extending beyond several wavelengths, ever-present interpolation and pollution errors degrade the predictions at a linear and nonlinear rate, respectively. As the number of wavelengths in the geometry increases, the nonlinear (pollution) term eventually dominates the approximation error. Prediction accuracy can be maintained by correspondingly increasing the number of elements per wavelength but at a cost of increasing computational need. This talk shall present an overview of interpolation and pollution errors and their effects, as well as a number of cutting-edge methodologies developed to overcome their influence in the mid-frequency range.