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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Stable spectral methods for conservation laws on triangles with pectral methods for conservation laws on triangles with unstructured grids
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Stable spectral methods for conservation laws on triangles with pectral methods for conservation laws on triangles with unstructured grids

机译：非结构网格上三角形守恒律的稳定谱方法

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摘要

This paper presents an asymptotically stable scheme for the spectral approximation of linear conservation laws defined on a triangle. Lagrange interpolation on a general two-dimensional nodal set is employed and, by imposing the boundary conditions weakly through a penalty term, the scheme is proven stable in L2. This result is established for a general unstructured grid in the triangle. A special case, for which the nodes along the edges of the triangle are chosen as the Legendre Gauss-Lobatto quadrature points, is discussed in detail. The eigenvalue spectrum of the approximation to the advective operator is computed and is shown to result in an al1 O(n~-2) restriction on the time-step when considering explicit time-stepping.
机译：本文为定义在三角形上的线性守恒定律的频谱逼近提出了一种渐近稳定的方案。采用拉格朗日插值法对普通二维节点集进行插值，并通过惩罚项对边界条件施加弱条件，该方法在L2中被证明是稳定的。对于三角形中的一般非结构化网格，可以确定该结果。详细讨论了一种特殊情况，即选择沿三角形边缘的节点作为Legendre Gauss-Lobatto正交点。计算对流算子的近似特征值谱，并显示出在考虑显式时间步长时会导致时间步长的alO（n〜-2）限制。

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