An adaptive strategy for hp-FEM based on testing for analyticity

We present an hp-adaptive strategy that is based on estimating the decay of the expansion coefficients when a function is expanded in L ²-orthogonal polynomials on a triangle or a tetrahedron. We justify this approach by showing that the decay of the coefficients is exponential if and only if the function is analytic. Numerical examples illustrate the performance of this approach, and we compare it with two other hp-adaptive strategies.