论文标题
指数网格和$ \ MATHCAL {H} $ - 矩阵
Exponential meshes and $\mathcal{H}$-matrices
论文作者
论文摘要
在我们以前的作品中，我们证明了应用于标量二阶椭圆形边界价值问题的$ h $ version有限元方法（fem）的刚度矩阵的倒数可以以$ \ nathcal {h} $ - 矩阵的指数速率以指数级的速率近似。在这里，我们以多种方式对此结果进行改进：（1）网格类已显着扩大，并包括某些指数分级的网格。 （2）在我们的分析中，对离散ansatz空间的多项式程度$ p $的依赖性表示。 （3）近似误差的结合被锐化，（4）简化了证明。
In our previous works, we proved that the inverse of the stiffness matrix of an $h$-version finite element method (FEM) applied to scalar second order elliptic boundary value problems can be approximated at an exponential rate in the block rank by $\mathcal{H}$-matrices. Here, we improve on this result in multiple ways: (1) The class of meshes is significantly enlarged and includes certain exponentially graded meshes. (2) The dependence on the polynomial degree $p$ of the discrete ansatz space is made explicit in our analysis. (3) The bound for the approximation error is sharpened, and (4) the proof is simplified.
