Continuous hp Finite Elements Based on Generalized Eigenfunctions

In this paper we present a new class of hp finite elements for product and simplicial geometries in R based on generalized eigenfunctions of the Laplace operator. Due to simultaneous orthogonality of the generalized eigenfunctions under both the H 0 and L 2 products, such finite elements have outstanding conditioning properties for second order elliptic problems. Analysis is accompanied by numerical examples, including comparisons to other popular sets of higher-order shape functions for both hp and spectral elements. AMS subject classification: 35B50, 65N60

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