A pollution-free ultra-weak FOSLS discretization of the Helmholtz equation

Harald Monsuur, R. Stevenson
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引用次数: 1

Abstract

We consider an ultra-weak first order system discretization of the Helmholtz equation. When employing the optimal test norm, the `ideal' method yields the best approximation to the pair of the Helmholtz solution and its scaled gradient w.r.t.~the norm on $L_2(\Omega)\times L_2(\Omega)^d$ from the selected finite element trial space. On convex polygons, the `practical', implementable method is shown to be pollution-free essentially whenever the order $\tilde{p}$ of the finite element test space grows proportionally with $\max(\log \kappa,p^2)$, with $p$ being the order at trial side. Numerical results also on other domains show a much better accuracy than for the Galerkin method.
亥姆霍兹方程的无污染超弱FOSLS离散化
考虑亥姆霍兹方程的超弱一阶系统离散化。当采用最优测试范数时,“理想”方法产生对亥姆霍兹解及其缩放梯度对的最佳近似值 $L_2(\Omega)\times L_2(\Omega)^d$ 从选定的有限元试验空间。在凸多边形上,“实用的”、可实现的方法被证明基本上是无公害的 $\tilde{p}$ 有限元的试验空间与之成正比增长 $\max(\log \kappa,p^2)$, with $p$ 作为审判方的命令。数值结果也表明,该方法在其他区域的精度比伽辽金方法高得多。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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