关于线性样条空间上的L_2投影算子的一个反例
A counterexample concerning the L_2-projector onto linear spline spaces
AI总结：
针对多面体域上单纯形剖分的线性样条空间，证明了L_2正交投影算子P的L_∞范数不能关于剖分一致有界，这与一维情况形成对比。
摘要：
对于R^d (d>1)中多面体域上单纯形剖分的线性样条空间上的L_2正交投影算子P，我们证明P的L_∞范数不能关于剖分一致有界。这与d=1的情况形成对比，在d=1时这些范数被3所界，与剖分无关。这一负面结果在有限元方法和逼近理论专家中广为流传，但似乎从未被正式证明。
英文摘要：
For the L_2-orthogonal projector P onto spaces of linear splines over simplicial partitions of polyhedral domains in R^d, d>1, we show that the L_infty norm of P cannot be bounded uniformly with respect to the partition. This is in contrast to d=1, where these norms are bounded by 3 independently of the partition. This negative result is folklore among specialists in finite element methods and approximation theory but seemingly has never been formally proved.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
