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Discontinuous Galerkin finite element methods for dynamic linear solid viscoelasticity problems
Author(s) -
Rivière Béatrice,
Shaw Simon,
Whiteman J.R.
Publication year - 2007
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.20215
Subject(s) - mathematics , finite element method , discontinuous galerkin method , galerkin method , discretization , a priori and a posteriori , viscoelasticity , partial differential equation , displacement (psychology) , mathematical analysis , element (criminal law) , physics , psychology , philosophy , epistemology , political science , law , psychotherapist , thermodynamics
We consider the usual linear elastodynamics equations augmented with evolution equations for viscoelastic internal stresses. A fully discrete approximation is defined, based on a spatially symmetric or non‐symmetric interior penalty discontinuous Galerkin finite element method, and a displacement‐velocity centred difference time discretisation. An a priori error estimate is given but only the main ideas in the proof of the error estimate are reported here due to the large number of (mostly technical) estimates that are required. The full details are referenced to a technical report. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007