Higher-order finite elements based on generalized eigenfunctions of the Laplacian

We present a new class of higher-order finite elements based on generalized eigenfunctions of the Laplace operator, which are suitable for both product and simplicial geometries in Rd . Due to simultaneous orthogonality of the generalized eigenfunctions under both the H1 0 and L2 products and their almost negligible dependence on reference maps, such finite elements are an excellent choice for the discretization of second-order elliptic problems by the hp-FEM. Analysis is illustrated by numerical results and comparisons with other popular higher-order finite elements are presented. The new elements are used to compute efficiently the model of an electrostatic micromotor. Copyright q 2007 John Wiley & Sons, Ltd.