A discrete analysis of the phase and dissipation errors of an explicit, semi-Lagrangian spectral element method is performed. The semi-Lagrangian method advects the Lagrange interpolant according the Lagrangian form of the transport equations and uses a least-square fit to correct the update for interface constraints of neighbouring elements. By assuming a monomial representation instead of the Lagrange form, a discrete version of the algorithm on a single element is derived. The resulting algebraic system lends itself to both a Modified Equation analysis and an eigenvalue analysis. The Modified Equation analysis, which Taylor expands the stencil at a single space location and time instance, shows that the semi-Lagrangian method is consistent with the PDE form of the transport equation in the limit that the element size goes to zero. The leading order truncation term of the Modified Equation is of the order of the degree of the interpolant which is consistent with numerical tests reported in the literature. The dispersion relations show that the method is negligibly dispersive, as is common for semi-Lagrangian methods. An eigenvalue analysis shows that the semi-Lagrangian method with a nodal Chebyshev interpolant is stable for a Courant-Friedrichs-Lewy condition based on the minimum collocation node spacing within an element that is greater than unity.

翻译：对一个清晰的半拉格朗日光谱元素法的相片和分解错误进行分解分析。 使用半拉格朗格方法, 以拉格朗格方程式的形式对拉格朗格线间线进行模拟分析, 并使用最差的方形来纠正相邻元素界面限制的更新。 通过假设单模表示法而不是拉格朗格形式, 得出一个单一元素的离异算法版本。 由此产生的正数系统既可以进行变异的方程分析, 也可以进行电子值分析。 调整的方形分析( 泰勒在单一空间方程式方程式和时间实例中扩展了斜方格间间线)显示, 半拉格方法符合元素大小为零的传输方形方格的PDE格式。 变异差法的偏差术语是比文献中报告的数值测试要高的内位值。 分散式关系分析显示, 离差法是固定的中间值, 该方法显示, 以不比正值为正值的中间值方法, 该方法显示, 该方法是用于普通的中间值。