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An adaptive strategy for \(hp\)-FEM based on testing for analyticity. (English) Zbl 1163.65331

Summary: 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.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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