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A generalized diagonal mass matrix spectral element method for non-quatrilateral elements. (English) Zbl 0964.65107
Summary: We introduce a Fekete point spectral element method. This is a generalization of the traditional quadrilateral based spectral element method to any general element such as triangles. It retains the exponential convergence and the diagonal mass matrix of the original method. We first solve a Sturm-Liouville problem in the square and the triangle to determine the correct functional space used for approximation. Once the functional space is known, we use the Fekete criterion to compute near optimal grids for these spaces which have the same number of points as the dimension of the functional space. This allows the construction of a well-behaved cardinal function basis which leads to a diagonal mass matrix.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35L45 Initial value problems for first-order hyperbolic systems
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