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 ℝ. Due to simultaneous orthogonality of the generalized eigenfunctions under both the H and L products and their almost...
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| Format: | Journal article |
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2008
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| Summary: | 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 ℝ. Due to simultaneous orthogonality of the generalized eigenfunctions under both the H and L 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 © 2007 John Wiley and Sons, Ltd. |
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