Abstract In this paper we present a simplified discussion of the Smoothness-Increasing Accuracy-Conserving (SIAC) filter. We demonstrate the importance of appropriately initializing the data in order to be able to extract higher orders of accuracy by comparing the nodal and modal forms of a discontinuous Galerkin approximation applied to a simplified cubic polynomial. Using the modal form, we are able to exactly reproduce the cubic polynomial, whereas this reconstruction does not occur using the nodal form. Furthermore, we tie the ability of the filter to extract extra accuracy to its accurate wave propagation properties.

中文翻译：

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使用卷积滤波器提高精度：什么有效以及为什么！

摘要 在本文中，我们对平滑度增加精度守恒 (SIAC) 滤波器进行了简化讨论。我们通过比较应用于简化三次多项式的不连续伽辽金近似的节点和模态形式，证明了适当初始化数据的重要性，以便能够提取更高阶的精度。使用模态形式，我们能够精确地重现三次多项式，而使用节点形式则不会发生这种重建。此外，我们将滤波器提取额外精度的能力与其准确的波传播特性联系起来。