1. Exponential meshes and $\mathcal{H}$-matrices
- Author
-
Angleitner, Niklas, Faustmann, Markus, and Melenk, Jens Markus
- Subjects
Mathematics - Numerical Analysis - Abstract
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.
- Published
- 2022
- Full Text
- View/download PDF