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A cut finite elemen...
A cut finite element method for the Bernoulli free boundary value problem
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- Burman, Erik (författare)
- University College London, Gower Street, UK
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- Elfverson, Daniel (författare)
- Umeå universitet,Institutionen för matematik och matematisk statistik,Umeå University, Sweden
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- Hansbo, Peter (författare)
- Jönköping University,JTH, Produktutveckling,JTH. Forskningsmiljö Produktutveckling - Simulering och optimering
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- Larson, Mats G. (författare)
- Umeå universitet,Institutionen för matematik och matematisk statistik,Umeå University, Sweden
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- Larsson, Karl (författare)
- Umeå universitet,Institutionen för matematik och matematisk statistik,Umeå University, Sweden
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(creator_code:org_t)
- Elsevier, 2017
- 2017
- Engelska.
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier. - 0045-7825 .- 1879-2138. ; 317, s. 598-618
- Relaterad länk:
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http://arxiv.org/pdf...
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https://urn.kb.se/re...
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https://doi.org/10.1...
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https://urn.kb.se/re...
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Abstract
Ämnesord
Stäng
- We develop a cut finite element method for the Bernoulli free boundary problem. The free boundary, represented by an approximate signed distance function on a fixed background mesh, is allowed to intersect elements in an arbitrary fashion. This leads to so called cut elements in the vicinity of the boundary. To obtain a stable method, stabilization terms are added in the vicinity of the cut elements penalizing the gradient jumps across element sides. The stabilization also ensures good conditioning of the resulting discrete system. We develop a method for shape optimization based on moving the distance function along a velocity field which is computed as the H1 Riesz representation of the shape derivative. We show that the velocity field is the solution to an interface problem and we prove an a priori error estimate of optimal order, given the limited regularity of the velocity field across the interface, for the velocity field in the H1norm. Finally, we present illustrating numerical results.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Nyckelord
- Free boundary value problem
- CutFEM
- Shape optimization
- Level set
- Fictitious domain method
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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