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A new approach to energy-based sparse FE spaces

by R. A. Todor

(Report number 2006-11)

Abstract
We show that the logarithmic factor in the standard error estimate for sparse FE spaces in arbitrary dimension $d$ is removable in the energy ($H^1$) norm. Via a penalized sparse grid condition, we then propose and analyse a new version of the energy-based sparse FE spaces introduced first in [Bun92] (see also [BG99]), and known to satisfy an optimal approximation property in the energy norm.

Keywords: sparse grids, multilevel methods, convergence rate

@Techreport{T06_360,
  author = {R. A. Todor},
  title = {A new approach to energy-based sparse FE spaces},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2006-11},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2006/2006-11.pdf },
  year = {2006}
}

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