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Adaptive Tree Approximation with Finite Element Functions: A First Look

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Numerical Methods for PDEs

Part of the book series: SEMA SIMAI Springer Series ((SEMA SIMAI,volume 15))

Abstract

We provide an introduction to adaptive tree approximation with finite element functions over meshes that are generated by bisection. This approximation technique can be seen as a benchmark for adaptive finite element methods, but may be also used therein for the approximation of data and coarsening. Correspondingly, we focus on approximation problems related to adaptive finite element methods, the design and performance of algorithms, and the resulting convergence rates, together with the involved regularity. For simplicity and clarity, these issues are presented and discussed in detail in the univariate case. The additional technicalities and difficulties of the multivariate case are briefly outlined.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Milano, Milano, Italy

    Andreas Veeser

Authors
  1. Andreas Veeser
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Correspondence to Andreas Veeser .

Editor information

Editors and Affiliations

  1. Institut Montpelliérain Alexander Grothendieck, CNRS, Université Montpellier, Montpellier, France

    Daniele Antonio Di Pietro

  2. Universit Paris Est, CERMICS (ENPC), Marne la Vallée, France

    Alexandre Ern

  3. MOX - Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Luca Formaggia

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Veeser, A. (2018). Adaptive Tree Approximation with Finite Element Functions: A First Look. In: Di Pietro, D., Ern, A., Formaggia, L. (eds) Numerical Methods for PDEs. SEMA SIMAI Springer Series, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-319-94676-4_9

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