Error estimates for the ultra weak variational formulation in linear elasticity

Teemu Luostari; Tomi Huttunen; Peter Monk

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2013)

  • Volume: 47, Issue: 1, page 183-211
  • ISSN: 0764-583X

Abstract

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We prove error estimates for the ultra weak variational formulation (UWVF) in 3D linear elasticity. We show that the UWVF of Navier’s equation can be derived as an upwind discontinuous Galerkin method. Using this observation, error estimates are investigated applying techniques from the theory of discontinuous Galerkin methods. In particular, we derive a basic error estimate for the UWVF in a discontinuous Galerkin type norm and then an error estimate in the L2(Ω) norm in terms of the best approximation error. Our final result is an L2(Ω) norm error estimate using approximation properties of plane waves to give an estimate for the order of convergence. Numerical examples are presented.

How to cite

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Luostari, Teemu, Huttunen, Tomi, and Monk, Peter. "Error estimates for the ultra weak variational formulation in linear elasticity." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.1 (2013): 183-211. <http://eudml.org/doc/273271>.

@article{Luostari2013,
abstract = {We prove error estimates for the ultra weak variational formulation (UWVF) in 3D linear elasticity. We show that the UWVF of Navier’s equation can be derived as an upwind discontinuous Galerkin method. Using this observation, error estimates are investigated applying techniques from the theory of discontinuous Galerkin methods. In particular, we derive a basic error estimate for the UWVF in a discontinuous Galerkin type norm and then an error estimate in the L2(Ω) norm in terms of the best approximation error. Our final result is an L2(Ω) norm error estimate using approximation properties of plane waves to give an estimate for the order of convergence. Numerical examples are presented.},
author = {Luostari, Teemu, Huttunen, Tomi, Monk, Peter},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {ultra weak variational formulation; error estimates; plane wave basis; linear elasticity; upwind discontinuous Galerkin method},
language = {eng},
number = {1},
pages = {183-211},
publisher = {EDP-Sciences},
title = {Error estimates for the ultra weak variational formulation in linear elasticity},
url = {http://eudml.org/doc/273271},
volume = {47},
year = {2013},
}

TY - JOUR
AU - Luostari, Teemu
AU - Huttunen, Tomi
AU - Monk, Peter
TI - Error estimates for the ultra weak variational formulation in linear elasticity
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2013
PB - EDP-Sciences
VL - 47
IS - 1
SP - 183
EP - 211
AB - We prove error estimates for the ultra weak variational formulation (UWVF) in 3D linear elasticity. We show that the UWVF of Navier’s equation can be derived as an upwind discontinuous Galerkin method. Using this observation, error estimates are investigated applying techniques from the theory of discontinuous Galerkin methods. In particular, we derive a basic error estimate for the UWVF in a discontinuous Galerkin type norm and then an error estimate in the L2(Ω) norm in terms of the best approximation error. Our final result is an L2(Ω) norm error estimate using approximation properties of plane waves to give an estimate for the order of convergence. Numerical examples are presented.
LA - eng
KW - ultra weak variational formulation; error estimates; plane wave basis; linear elasticity; upwind discontinuous Galerkin method
UR - http://eudml.org/doc/273271
ER -

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