论文标题
振荡函数的分段多项式近似的下限
Lower bounds for piecewise polynomial approximations of oscillatory functions
论文作者
论文摘要
当使用分段多项式空间近似任何振荡函数时，我们证明了误差的下限。估计值在多项式程度上是显式的，并且在固定多项式程度时对网状和频率具有最佳的依赖性。例如，这些下限应用于将解决方案近似于Helmholtz平面波散射问题。
We prove lower bounds on the error incurred when approximating any oscillating function using piecewise polynomial spaces. The estimates are explicit in the polynomial degree and have optimal dependence on the meshwidth and frequency when the polynomial degree is fixed. These lower bounds, for example, apply when approximating solutions to Helmholtz plane wave scattering problem.
