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.
Mots clés : ultra weak variational formulation, error estimates, plane wave basis, linear elasticity, upwind discontinuous Galerkin method
@article{M2AN_2013__47_1_183_0,
author = {Luostari, Teemu and Huttunen, Tomi and Monk, Peter},
title = {Error estimates for the ultra weak variational formulation in linear elasticity},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {183--211},
publisher = {EDP-Sciences},
volume = {47},
number = {1},
year = {2013},
doi = {10.1051/m2an/2012025},
mrnumber = {2979514},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2012025/}
}
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 PY - 2013 SP - 183 EP - 211 VL - 47 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2012025/ DO - 10.1051/m2an/2012025 LA - en ID - M2AN_2013__47_1_183_0 ER -
%0 Journal Article %A Luostari, Teemu %A Huttunen, Tomi %A Monk, Peter %T Error estimates for the ultra weak variational formulation in linear elasticity %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %P 183-211 %V 47 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2012025/ %R 10.1051/m2an/2012025 %G en %F M2AN_2013__47_1_183_0
Luostari, Teemu; Huttunen, Tomi; Monk, Peter. Error estimates for the ultra weak variational formulation in linear elasticity. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 1, pp. 183-211. doi : 10.1051/m2an/2012025. http://archive.numdam.org/articles/10.1051/m2an/2012025/
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