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Error estimates for...
Error estimates for finite element approximations of viscoelastic dynamics : the generalized Maxwell model
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- Björklund, Martin (författare)
- Umeå universitet,Institutionen för matematik och matematisk statistik
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- Larsson, Karl, 1981- (författare)
- Umeå universitet,Institutionen för matematik och matematisk statistik
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- Larson, Mats G. (författare)
- Umeå universitet,Institutionen för matematik och matematisk statistik
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(creator_code:org_t)
- Elsevier, 2024
- 2024
- Engelska.
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier. - 0045-7825 .- 1879-2138. ; 425
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Abstract
Ämnesord
Stäng
- We prove error estimates for a finite element approximation of viscoelastic dynamics based on continuous Galerkin in space and time, both in energy norm and in L2 norm. The proof is based on an error representation formula using a discrete dual problem and a stability estimate involving the kinetic, elastic, and viscoelastic energies. To set up the dual error analysis and to prove the basic stability estimates, it is natural to formulate the problem as a first-order-in-time system involving evolution equations for the viscoelastic stress, the displacements, and the velocities. The equations for the viscoelastic stress can, however, be solved analytically in terms of the deviatoric strain velocity, and therefore, the viscoelastic stress can be eliminated from the system, resulting in a system for displacements and velocities.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Nyckelord
- Viscoelasticity
- Generalized Maxwell solid
- Finite element method
- A priori error analysis
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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