Exponential meshes and H-matrices

被引：1
|
作者：
Angleitner, Niklas [1 ]
Faustmann, Markus [1 ]
Melenk, Jens Markus [1 ]
机构：
[1] Tech Univ Wien, Inst Anal & Sci Comp Inst E 101, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2023年 / 130卷
基金：
奥地利科学基金会;
关键词：
FEM; H-matrices; Approximability; Non-uniform meshes; PROJECTION-BASED INTERPOLATION; BEM MATRICES; P-VERSION; APPROXIMATION; EXISTENCE; INVERSES; FEM; APPROXIMABILITY;
D O I：
10.1016/j.camwa.2022.11.011
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In [1], 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.
引用
收藏
页码：21 / 40
页数：20
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