Exponential meshes and ℋ-matrices

03/18/2022

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by   Niklas Angleitner, et al.

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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 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.