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A cut finite element method for elliptic bulk problems with embedded surfaces
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- Burman, Erik (author)
- Mathematics, University College London, London, United Kingdom
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- Hansbo, Peter (author)
- Jönköping University,JTH, Material och tillverkning
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- Larson, Mats G. (author)
- Umeå universitet,Institutionen för matematik och matematisk statistik,Mathematics and Mathematical Statistics, Umeå University, Umeå, Sweden
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- (creator_code:org_t)
- 2019-01-29
- 2019
- English.
- In: GEM - International Journal on Geomathematics. - : Springer. - 1869-2672 .- 1869-2680. ; 10:1
- Journal article (peer-reviewed)
Abstract
Subject headings
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- We propose an unfitted finite element method for flow in fractured porous media. The coupling across the fracture uses a Nitsche type mortaring, allowing for an accurate representation of the jump in the normal component of the gradient of the discrete solution across the fracture. The flow field in the fracture is modelled simultaneously, using the average of traces of the bulk variables on the fractures. In particular the Laplace–Beltrami operator for the transport in the fracture is included using the average of the projection on the tangential plane of the fracture of the trace of the bulk gradient. Optimal order error estimates are proven under suitable regularity assumptions on the domain geometry. The extension to the case of bifurcating fractures is discussed. Finally the theory is illustrated by a series of numerical examples.
Subject headings
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
- NATURVETENSKAP -- Data- och informationsvetenskap -- Datavetenskap (hsv//swe)
- NATURAL SCIENCES -- Computer and Information Sciences -- Computer Sciences (hsv//eng)
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
Keyword
- Embedded
- Finite element
- Fractures
- Unfitted
- Fracture
- Porous materials
- Domain geometry
- Embedded surfaces
- Fractured porous media
- Normal component
- Optimal order error estimates
- Regularity assumption
- Finite element method
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- ref (subject category)
- art (subject category)
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- Larson, Mats G.
- Samvin, David
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