A generalized diagonal mass matrix spectral element method for non-quadrilateral elements

We introduce a Fekete point spectral element method. This is a generalizati on of the traditional quadrilateral based spectral element method to any ge neral element such as triangles. It retains the exponential convergence and the diagonal mass matrix of the original method. We first solve a Sturm-Li ouville problem in the square and the triangle to determine the correct fun ctional space used for approximation. Once the functional space is known, w e use the Fekete criterion to compute near optimal grids for these spaces w hich have the same number of points as the dimension of the functional spac e. This allows the construction of a well-behaved cardinal function basis w hich leads to a diagonal mass matrix. (C) 2000 IMACS. Published by Elsevier Science B.V. All rights reserved.