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Error estimates for the ultra weak variational formulation inlinear elasticity∗

Published online by Cambridge University Press:  31 August 2012

Teemu Luostari ,
Tomi Huttunen  and
Peter Monk
Teemu Luostari
Affiliation:
Department of Applied Physics, University of Eastern Finland P.O. Box 1627, 70211 Kuopio, Finland. teemu.luostari@uef.fi; tomi.huttunen@uef.fi
Tomi Huttunen
Affiliation:
Department of Applied Physics, University of Eastern Finland P.O. Box 1627, 70211 Kuopio, Finland. teemu.luostari@uef.fi; tomi.huttunen@uef.fi
Peter Monk
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, 19716 DE, USA.; monk@math.udel.edu
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Abstract

We prove error estimates for the ultra weak variational formulation (UWVF) in 3D linearelasticity. We show that the UWVF of Navier’s equation can be derived as an upwinddiscontinuous Galerkin method. Using this observation, error estimates are investigatedapplying techniques from the theory of discontinuous Galerkin methods. In particular, wederive a basic error estimate for the UWVF in a discontinuous Galerkin type norm and thenan error estimate in the L2(Ω) norm in terms of the bestapproximation error. Our final result is an L2(Ω) norm errorestimate using approximation properties of plane waves to give an estimate for the orderof convergence. Numerical examples are presented.

Keywords

Ultra weak variational formulationerror estimatesplane wave basislinear elasticityupwind discontinuous Galerkin method
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 1 , January 2013 , pp. 183 - 211
Copyright
© EDP Sciences, SMAI, 2012

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