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Stabilized CutFEM f...
Stabilized CutFEM for the convection problem on surfaces
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- Burman, Erik (författare)
- UCL, Dept Math, London WC1E 6BT, England.,UCL, Department of Mathematics, London, United Kingdom
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- Hansbo, Peter (författare)
- Jönköping University,JTH, Material och tillverkning
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- Larson, Mats G. (författare)
- Umeå universitet,Institutionen för matematik och matematisk statistik,Umea Univ, Dept Math & Math Stat, S-90187 Umea, Sweden.,Umeå Universitet, Department of Mathematics and Mathematical Statistics, Umeå, Sweden
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- Zahedi, Sara, 1981- (författare)
- KTH,Matematik (Inst.),The Royal Institute of Technology (KTH), Department of Mathematics, Stockholm, Sweden
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UCL, Dept Math, London WC1E 6BT, England UCL, Department of Mathematics, London, United Kingdom (creator_code:org_t)
- 2018-08-18
- 2019
- Engelska.
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Ingår i: Numerische Mathematik. - : Springer Berlin/Heidelberg. - 0029-599X .- 0945-3245. ; 141:1, s. 103-139
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Abstract
Ämnesord
Stäng
- We develop a stabilized cut finite element method for the convection problem on a surface based on continuous piecewise linear approximation and gradient jump stabilization terms. The discrete piecewise linear surface cuts through a background mesh consisting of tetrahedra in an arbitrary way and the finite element space consists of piecewise linear continuous functions defined on the background mesh. The variational form involves integrals on the surface and the gradient jump stabilization term is defined on the full faces of the tetrahedra. The stabilization term serves two purposes: first the method is stabilized and secondly the resulting linear system of equations is algebraically stable. We establish stability results that are analogous to the standard meshed flat case and prove h3/2 order convergence in the natural norm associated with the method and that the full gradient enjoys h3/4 order of convergence in L2. We also show that the condition number of the stiffness matrix is bounded by h-2. Finally, our results are verified by numerical examples.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
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