Exponential meshes and $\mathcal{H}$-matrices

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.

References in corpus (6)

• H-matrix approximability of the inverses of FEM matrices
• On commuting $p$-version projection-based interpolation on tetrahedra
• Existence of $\mathcal{H}$-matrix approximants to the inverses of BEM matrices: the simple-layer operator
• Optimal additive Schwarz methods for the $hp$-BEM: the hypersingular integral operator in 3D on locally refined meshes
• Mortar coupling of $hp$-discontinuous Galerkin and boundary element methods for the Helmholtz equation
• Caccioppoli-type estimates and $\mathcal{H}$-Matrix approximations to inverses for FEM-BEM couplings

Cited by in corpus (1)

• $\mathcal{H}$-inverses for RBF interpolation