Modified integration rules for reducing dispersion error in finite element methods

This paper describes a simple but effective technique for reducing dispersion errors in finite element solutions of time-harmonic wave propagation problems. The method involves a simple shift of the integration points to locations away from conventional Gauss or Gauss-Lobatto integration points. For bilinear rectangular elements, such a shift results in fourth-order accuracy with respect to dispersion error (error in wavelength), as opposed to the second-order accuracy resulting from conventional integration. Numerical experiments involving distorted meshes indicate that the method has superior performance in comparison with other dispersion reducing finite elements. (C) 2003 Elsevier B.V. All rights reserved.