A residual-based finite element method for the Helmholtz equation

A new residual-based finite element method for the scalar Helmholtz equatio n is developed. This method is obtained from the Galerkin approximation by appending terms that are proportional to residuals on element interiors and inter-element boundaries. The inclusion of residuals on inter-element boun daries distinguishes this method from the well-known Galerkin least-squares method and is crucial to the resulting accuracy of this method. In two dim ensions and for regular bilinear quadrilateral finite elements, it is shown via a dispersion analysis that this method has minimal phase error. Numeri cal experiments are conducted to verify this claim as well as test and comp are the performance of this method on unstructured meshes with other method s. It is found that even for unstructured meshes this method retains a high level of accuracy. Copyright (C) 2000 John Wiley & Sons, Ltd.