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• W1678850202 abstract "This paper develops and analyzes some continuous interior penalty finite element methods (CIP-FEMs) using piecewise linear polynomials for the Helmholtz equation with the first order absorbing boundary condition in two and three dimensions. The novelty of the proposed methods is to use complex penalty parameters with positive imaginary parts. It is proved that, if the penalty parameter is a pure imaginary number $iga$ with $0 C_0$ and $kh$ is bounded, where $k$ is the wave number, $h$ is the mesh size, and the $C$'s are positive constants independent of $k$, $h$, and $ga$. Optimal order $L^2$ error estimates are also derived. The analysis is also applied if the penalty parameter is a complex number with positive imaginary part. By taking $gato 0+$, the above estimates are extended to the linear finite element method under the condition $k^3h^2le C_0$. Numerical results are provided to verify the theoretical findings. It is shown that the penalty parameters may be tuned to greatly reduce the pollution errors." @default.
• W1678850202 created "2016-06-24" @default.
• W1678850202 creator A5034214957 @default.
• W1678850202 date "2011-06-21" @default.
• W1678850202 modified "2023-09-24" @default.
• W1678850202 title "Continuous Interior Penalty Finite Element Methods for the Helmholtz Equation with Large Wave Number" @default.
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