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A posteriori error estimates for discontinuous Galerkin method to the elasticity problem
Author(s) -
Luong Thi Hong Cam,
Daveau Christian
Publication year - 2018
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22261
Subject(s) - a priori and a posteriori , mathematics , elasticity (physics) , backward euler method , linear elasticity , galerkin method , mathematical optimization , discontinuous galerkin method , finite element method , euler equations , mathematical analysis , philosophy , physics , epistemology , thermodynamics , materials science , composite material
This work concerns with the discontinuous Galerkin (DG) method for the time‐dependent linear elasticity problem. We derive the a posteriori error bounds for semidiscrete and fully discrete problems, by making use of the stationary elasticity reconstruction technique which allows to estimate the error for time‐dependent problem through the error estimation of the associated stationary elasticity problem. For fully discrete scheme, we make use of the backward‐Euler scheme and an appropriate space‐time reconstruction. The technique here can be applicable for a variety of DG methods as well.