# Error estimates for the ultra weak variational formulation in linear elasticity∗

Teemu Luostari; Tomi Huttunen; Peter Monk

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

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

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topLuostari, Teemu, Huttunen, Tomi, and Monk, Peter. "Error estimates for the ultra weak variational formulation in linear elasticity∗." ESAIM: Mathematical Modelling and Numerical Analysis 47.1 (2012): 183-211. <http://eudml.org/doc/222157>.

@article{Luostari2012,

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},

keywords = {Ultra weak variational formulation; error estimates; plane wave basis; linear elasticity; upwind discontinuous Galerkin method; ultra weak variational formulation},

language = {eng},

month = {8},

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/222157},

volume = {47},

year = {2012},

}

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

DA - 2012/8//

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; ultra weak variational formulation

UR - http://eudml.org/doc/222157

ER -

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