Extension of a Post Processing Technique for the Discontinuous Galerkin Method for Hyperbolic Equations with Application to an Aeroacoustic Problem
Extension of a Post Processing Technique for the Discontinuous Galerkin Method for Hyperbolic Equations with Application to an Aeroacoustic Problem
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DOI：
10.1137/s1064827503423998
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发表时间：
2005-03
期刊：
影响因子：
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通讯作者：
J. Ryan;Chi-Wang Shu;H. Atkins
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文献类型：
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作者：
J. Ryan;Chi-Wang Shu;H. Atkins
在这篇文章中，我们进一步探索了一种局部后处理技术，最初由Bramble和Schatz[Math.Comp.，31(1977)，pp.94--111]使用连续有限元方法求解椭圆型问题，后来由Cockburn等人提出。[数学。Comp.72(2003)，pp.577--606]使用双曲型方程的间断Galerkin方法。我们在数值解、张量积局部基和通常的K次多项式基的两个空间维、不同网格尺寸的多区域问题、变系数线性问题(包括具有间断系数的变系数线性问题)以及线性化的Euler方程应用于气动声学问题的背景下研究了这一技巧。通过大量的数值算例表明，该方法在提高间断Galerkin解的精度方面是非常有效的。
In this paper we further explore a local postprocessing technique, originally developed by Bramble and Schatz [Math. Comp., 31 (1977), pp. 94--111] using continuous finite element methods for elliptic problems and later by Cockburn et al. [Math. Comp., 72 (2003), pp. 577--606] using discontinuous Galerkin methods for hyperbolic equations. We investigate the technique in the context of superconvergence of the derivatives of the numerical solution, two space dimensions for both tensor product local basis and the usual kth degree polynomials basis, multidomain problems with different mesh sizes, variable coefficient linear problems including those with discontinuous coefficients, and linearized Euler equations applied to an aeroacoustic problem. We demonstrate through extensive numerical examples that the technique is very effective in all these situations in enhancing the accuracy of the discontinuous Galerkin solutions.