| 1. |
- Hansbo, Peter F G, 1959, et al.
(författare)
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An adaptive low-order FE-scheme for Stokes flow with cavitation
- 2010
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Ingår i: Journal of Numerical Mathematics. - 1570-2820 .- 1569-3953. ; 18:3, s. 177-185
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Tidskriftsartikel (refereegranskat)abstract
- In this note we derive a posteriori error bounds for FE-discretisations for a fluid problem with cavitation. The underlying model is the Stokes system together with an inequality constraint for the pressure. In order to avoid suboptimal behavior of the error bounds we propose to employ a Lagrange setting yielding an improved estimate. Numerical tests confirm our theoretical results.
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| 2. |
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| 3. |
- Burman, Erik, 1968, et al.
(författare)
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Fictitious domain finite element methods using cut elements: I. A stabilized Lagrange multiplier method
- 2010
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825 .- 1879-2138. ; 199:41-44, s. 2680-2686
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Tidskriftsartikel (refereegranskat)abstract
- We propose a fictitious domain method where the mesh is cut by the boundary. The primal solution is computed only up to the boundary; the solution itself is defined also by nodes outside the domain, but the weak finite element form only involves those parts of the elements that are located inside the domain. The multipliers are defined as being element-wise constant on the whole (including the extension) of the cut elements in the mesh defining the primal variable. Inf–sup stability is obtained by penalizing the jump of the multiplier over element faces. We consider the case of a polygonal domain with possibly curved boundaries. The method has optimal convergence properties.
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| 4. |
- Burman, Erik, 1968, et al.
(författare)
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Interior-penalty-stabilized Lagrange multiplier methods for the finite-element solution of elliptic interface problems
- 2010
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Ingår i: IMA Journal of Numerical Analysis. - : Oxford University Press (OUP). - 0272-4979 .- 1464-3642. ; 30:3, s. 870-885
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we propose a class of jump-stabilized Lagrange multiplier methods for the finite-element solution of multidomain elliptic partial differential equations using piecewise-constant or continuous piecewise-linear approximations of the multipliers. For the purpose of stabilization we use the jumps in derivatives of the multipliers or, for piecewise constants, the jump in the multipliers themselves, across element borders. The ideas are illustrated using Poisson's equation as a model, and the proposed method is shown to be stable and optimally convergent. Numerical experiments demonstrating the theoretical results are also presented.
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| 5. |
- Hansbo, Peter F G, 1959
(författare)
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A discontinuous finite element method for elasto-plasticity
- 2010
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Ingår i: International Journal for Numerical Methods in Biomedical Engineering. - : Wiley. - 2040-7939 .- 2040-7947. ; 26:6, s. 780-789
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Tidskriftsartikel (refereegranskat)abstract
- We propose an interior penalty discontinuous finite element method for small strain elasto-plasticity using triangular or tetrahedral meshes. A new penalty formulation suitable for plasticity, in particular allowing for inter-element slip, is introduced. The method is also locking free, which is crucial as the plastic zone may exhibit an incompressible response. Numerical results are presented.
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| 6. |
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| 7. |
- Hansbo, Peter F G, 1959, et al.
(författare)
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A linear nonconforming finite element method for Maxwell's equations in two dimensions. Part I: Frequency domain
- 2010
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Ingår i: Journal of Computational Physics. - : Elsevier BV. - 0021-9991 .- 1090-2716. ; 229:18, s. 6534-6547
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Tidskriftsartikel (refereegranskat)abstract
- We suggest a linear nonconforming triangular element for Maxwell’s equations and test it in the context of the vector Helmholtz equation. The element uses discontinuous normal fields and tangential fields with continuity at the midpoint of the element sides, an approximation related to the Crouzeix–Raviart element for Stokes. The element is stabilized using the jump of the tangential fields, giving us a free parameter to decide. We give dispersion relations for different stability parameters and give some numerical examples, where the results converge quadratically with the mesh size for problems with smooth boundaries. The proposed element is free from spurious solutions and, for cavity eigenvalue problems, the eigenfrequencies that correspond to well-resolved eigenmodes are reproduced with the correct multiplicity.
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| 9. |
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| 10. |
- Hansbo, Peter F G, 1959, et al.
(författare)
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An adaptive finite element method for second order plate theory
- 2010
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 81:5, s. 584-603
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Tidskriftsartikel (refereegranskat)abstract
- We present a discontinuous finite element method for the Kirchhoff plate model with membrane stresses. The method is based on P2-approximations on simplices for the out-of-plane deformations, using C0-continuous approximations. We derive a posteriori error estimates for linear functionals of the error and give some numerical examples.
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