HIGH-ORDER FINITE-ELEMENT METHODS FOR ACOUSTIC PROBLEMS

The goal of this work is to design and analyze quadratic finite elemen ts for problems of time-harmonic acoustics, and to compare the computa tional efficiency of quadratic elements to that of lower-order element s. Non-reflecting boundary conditions yield an equivalent problem in a bounded region which is suitable for domain-based computation of solu tions to exterior problems. Galerkin/least-squares technology is utili zed to develop robust methods in which stability properties are enhanc ed while maintaining higher-order accuracy. The design of Galerkin/lea st-squares methods depends on the order of interpolation employed, and in this case quadratic elements are designed to yield dispersion-free solutions to model problems. The accuracy of Galerkin/least-squares a nd traditional Galerkin elements is compared, as well as the accuracy of quadratic Versus standard linear interpolation, incorporating the e ffects of representing the radiation condition in exterior problems. T he efficiency of the various methods is measured in terms of the cost of computation, rather than resolution requirements. In this manner, c lear guidelines for selecting the order of interpolation are derived. Numerical testing validates the superior performance of the proposed m ethods. This work is a first step to gaining a thorough analytical und erstanding of the performance of p refinement as a basis for the devel opment of h-p finite element methods for large-scale computation of so lutions to acoustic problems.