Adaptive aggregation on graphs

Abstract

We generalize some of the functional (hyper-circle) a posteriori estimates from finite element settings to general graphs or Hilbert space settings. We provide several theoretical results in regard to the generalized a posteriori error estimators. We use these estimates to construct aggregation based coarse spaces for graph Laplacians. The estimator is used to assess the quality of an aggregation adaptively. Furthermore, a reshaping algorithm based is tested on several numerical examples.

17 pages

References in corpus (1)

• Discrete $p$-robust $\mathbf{H}(\mathrm{div})$-liftings and a posteriori estimates for elliptic problems with $H^{-1}$ source terms

Cited by in corpus (3)

• Automatic coarsening in Algebraic Multigrid utilizing quality measures for matching-based aggregations
• Smoother-type a posteriori error estimates for finite element methods
• A Posteriori Error Estimates for Solving Graph Laplacians