ABSTRACT The representation of a force or moment point source in a spectral finite‐element code for modelling elastic wave propagation becomes fundamentally different in degenerate cases where the source is located on the boundary of an element. This difference is related to the fact that the finite‐element basis functions are continuous across element boundaries, but their derivatives are not. A method is presented that effectively deals with this problem. Tests on one‐dimensional elements show that the numerical errors for a force source follow the expected convergence rate in terms of the element size, apart from isolated cases where superconvergence occurs. For a moment source, the method also converges but one order of accuracy is lost, probably because of the reduced regularity of the problem. Numerical tests in three dimensions on continuous mass‐lumped tetrahedral elements show a similar error behaviour as in the one‐dimensional case, although in three dimensions the loss of accuracy for the moment source is not a severe as a full order.

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研究笔记：关于单纯谱有限元中力源和力矩源的误差行为

摘要 在用于模拟弹性波传播的谱有限元代码中，力或力矩点源的表示在源位于单元边界的退化情况下变得根本不同。这种差异与这样一个事实有关，即有限元基函数跨单元边界是连续的，但它们的导数不是。提出了一种有效处理该问题的方法。对一维单元的测试表明，除了发生超收敛的个别情况外，力源的数值误差在单元尺寸方面遵循预期的收敛速度。对于矩源，该方法也收敛，但损失一个数量级的精度，可能是因为问题的规律性降低。