Exponential meshes and $\mathcal{H}$-matrices
Numerical Analysis
2024-07-25 v1 Numerical Analysis
Abstract
In our previous works, we proved that the inverse of the stiffness matrix of an -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 -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 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.
Cite
@article{arxiv.2203.09925,
title = {Exponential meshes and $\mathcal{H}$-matrices},
author = {Niklas Angleitner and Markus Faustmann and Jens Markus Melenk},
journal= {arXiv preprint arXiv:2203.09925},
year = {2024}
}