On the solution of boundary value problems by the spectral element method
Keywords:
spectral element method, the Poisson equation, Dirichlet boundary conditions, Galerkin formulation, orthogonal functions, orthogonal polynomials, Legendre polynomials, Bubble functions, Lagrange polynomialsAbstract
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 spectral 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.
