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, uN 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 .
Read more about this topic: Spectral Element Method
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