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High Quality Content by WIKIPEDIA articles! In mathematics, the spectral element method is a high order finite element method. Introduced in a 1984 paper by A. T. Patera, the abstract begins: "A spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques..." The spectral element method is an elegant formulation of the finite element method with a high degree piecewise polynomial basis. The spectral method expands the solution in trigonometric series, a chief advantage is that the resulting method is of very high order. This approach relies on the fact that trigonometric polynomials are an orthonormal basis for L2( ). The spectral element method chooses instead high degree piecewise polynomial basis functions, also achieving a very high order of accuracy.