Spectral Element Method - A-priori Error Estimate

A-priori Error Estimate

The classic analysis of Galerkin methods and Céa's lemma holds here and it can be shown that, if u is the solution of the weak equation, u_N is the approximate solution and :

where C is independent from N and s is no larger than the degree of the piecewise polynomial basis. As we increase N, we can also increase the degree of the basis functions. In this case, if u is an analytic function:

where depends only on .