指数网格和h矩阵

Comput. Math. Appl. Pub Date : 2023-01-01 DOI:10.48550/arXiv.2203.09925

Niklas Angleitner, M. Faustmann, J. Melenk

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引用次数: 2

摘要

。在[AFM21a]中，我们证明了用于标量二阶椭圆型边值问题的h型有限元法的刚度矩阵逆可以用h -矩阵在块阶上以指数速率逼近。在这里，我们通过多种方式改进了这一结果:(1)网格的类别显着扩大，并包括某些指数级分级网格。(2)在我们的分析中明确了离散方差空间对多项式次p的依赖性。(3)锐化了近似误差的界;(4)简化了证明。

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Exponential meshes and H-matrices

. In [AFM21a], 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 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.

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Comput. Math. Appl.

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