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IMA Journal of Numerical Analysis Advance Access originally published online on February 16, 2008
IMA Journal of Numerical Analysis 2009 29(1):72-85; doi:10.1093/imanum/drm041
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

A new approach to energy-based sparse finite-element spaces

Radu-Alexandru Todor{dagger}

Seminar for Applied Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zurich, Switzerland

{dagger} Email: todor{at}math.ethz.ch

Received on 19 May 2006. Revised on 4 November 2007.


  Abstract

We show that the logarithmic factor in the standard error estimate for sparse finite element (FE) spaces in arbitrary dimension d is removable in the energy (H1) 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 Bungartz (1992, Dünne Gitter und deren Anwendung bei der adaptiven Lösung der dreidimensionalen Poisson-Gleichung. Dissertation. Munich, Germany: TU München) and known to satisfy an optimal approximation property in the energy norm.

Key Words: sparse grids; multilevel methods; convergence rate


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