Dispersion Analysis of CIP-FEM for Helmholtz Equation
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When solving the Helmholtz equation numerically, the accuracy of numerical solution deteriorates as the wave number k increases, known as `pollution effect' which is directly related to the phase difference between the exact and numerical solutions, caused by the numerical dispersion. In this paper, we propose a dispersion analysis for the continuous interior penalty finite element method (CIP-FEM) and derive an explicit formula of the penalty parameter for the p^ th order CIP-FEM on tensor product (Cartesian) meshes, with which the phase difference is reduced from 𝒪(k(kh)^2p) to 𝒪(k(kh)^2p+2). Extensive numerical tests show that the pollution error of the CIP-FE solution is also reduced by two orders in kh with the same penalty parameter.
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