On the solution of boundary value problems by the spectral element method

Abstract

In spectral element method approximate solution of the original differential operator is found in the form of a combination of the linearly independent system of orthogonal functions on the unit interval. Using the spec-tral decomposition for sufficiently smooth functions, one can obtain an exponential rate of convergence of the approximate solution to the exact solution and the approximation error will decrease exponentially as n grows. In the article the application of spectral element method to the solution of the boundary value problem for the Poisson equation is presented.