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Stable mixed finite...
Stable mixed finite elements for linear elasticity with thin inclusions
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- Boon, Wietse M. (författare)
- KTH,Numerisk analys, NA,Institute for Modelling Hydraulic and Environmental Systems, University of Stuttgart, Stuttgart, 70569, Germany
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Nordbotten, J. M. (författare)
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(creator_code:org_t)
- 2020-11-06
- 2021
- Engelska.
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Ingår i: Computational Geosciences. - : Springer Nature. - 1420-0597 .- 1573-1499. ; 25:2, s. 603-620
- Relaterad länk:
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https://doi.org/10.1...
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https://link.springe...
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of hierarchically connected manifolds is formed which we refer to as mixed-dimensional. The governing equations with respect to linear elasticity are then defined on this mixed-dimensional geometry. The resulting system of partial differential equations is also referred to as mixed-dimensional, since functions defined on domains of multiple dimensionalities are considered in a fully coupled manner. With the use of a semi-discrete differential operator, we obtain the variational formulation of this system in terms of both displacements and stresses. The system is then analyzed and shown to be well-posed with respect to appropriately weighted norms. Numerical discretization schemes are proposed using well-known mixed finite elements in all dimensions. The schemes conserve linear momentum locally while relaxing the symmetry condition on the stress tensor. Stability and convergence are shown using a priori error estimates and confirmed numerically.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Nyckelord
- A priori analysis
- Linear elasticity
- Mixed finite element
- Mixed-dimensional
- Weak symmetry
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- art (ämneskategori)
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