Wavenumber-explicit convergence of the hp-FEM for the full-space heterogeneous Helmholtz equation with smooth coefficients
Computers & Mathematics with Applications(2022)
摘要
A convergence theory for the hp-FEM applied to a variety of constant-coefficient Helmholtz problems was pioneered in the papers [35], [36], [15], [34]. This theory shows that, if the solution operator is bounded polynomially in the wavenumber k, then the Galerkin method is quasioptimal provided that hk/p≤C1 and p≥C2logk, where C1 is sufficiently small, C2 is sufficiently large, and both are independent of k,h, and p. The significance of this result is that if hk/p=C1 and p=C2logk, then quasioptimality is achieved with the total number of degrees of freedom proportional to kd; i.e., the hp-FEM does not suffer from the pollution effect.
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关键词
Helmholtz equation,hp-FEM,High frequency,Pollution effect
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