Nodal Interpolation Between First-Order Finite Element Spaces in 1D is Uniformly H 1-Stable

T. Dickopf ()
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T. Dickopf: University of Lugano, Institute of Computational Science

A chapter in Numerical Mathematics and Advanced Applications 2011, 2013, pp 419-427 from Springer

Abstract: Abstract This paper is about the stability w.r.t. the H 1-semi-norm of the nodal interpolation operator acting between non-nested finite element spaces. (An earlier, slightly less general version of the main result has been proved in the author’s thesis (Dickopf, Multilevel methods based on non-nested meshes. Ph.D. thesis, University of Bonn, 2010. http://hss.ulb.uni-bonn.de/2010/2365 , Chap. 5.1). Lively and fruitful discussions first during the ENUMATH conference in September and then during the Söllerhaus Workshop on Domain Decomposition Methods in October 2011 have encouraged the author to rework the analysis of the nodal interpolation over intervals and present it in this extended and considerably revised form.) We show that, for arbitrary spaces of piecewise linear functions of one variable, the H 1-stability constant is bounded by one without any assumptions on the mesh sizes or on the relations between the meshes. We also give counterexamples for the nodal interpolation in higher order finite element spaces.

Keywords: Interpolation Nodes; Higher Order Finite Element Spaces; Nodal Interpolation Operator; Piecewise Linear Function; Domain Decomposition Methods (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-33134-3_45

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DOI: 10.1007/978-3-642-33134-3_45

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