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- 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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| 3. |
- Hansbo, Peter F G, 1959, et al.
(författare)
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A finite element method with discontinuous rotations for the Mindlin-Reissner plate model
- 2011
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825 .- 1879-2138. ; 200:5-8, s. 638-648
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Tidskriftsartikel (refereegranskat)abstract
- We present a continuous-discontinuous finite element method for the Mindlin-Reissner plate model based on continuous polynomials of degree k >= 2 for the transverse displacements and discontinuous polynomials of degree k - 1 for the rotations. We prove a priori convergence estimates, uniformly in the thickness of the plate, and thus show that locking is avoided. We also derive a posteriori error estimates based on duality, together with corresponding adaptive procedures for controlling linear functionals of the error. Finally, we present some numerical results.
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| 5. |
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| 6. |
- Hansbo, Peter F G, 1959, et al.
(författare)
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A posteriori error estimates for continuous/discontinuous Galerkin approximations of the Kirchhoff-Love plate
- 2011
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - Amsterdam : Elsevier BV. - 0045-7825 .- 1879-2138. ; 200:47-48, s. 3289-3295
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Tidskriftsartikel (refereegranskat)abstract
- We present energy norm a posteriori error estimates for continuous/discontinuous Galerkin (c/dG) approximations of the Kirchhoff-Love plate problem. The method is based on a continuous displacement field inserted into a symmetric discontinuous Galerkin formulation of the fourth order partial differential equation governing the deflection of a thin plate. We also give explicit formulas for the penalty parameter involved in the formulation.
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| 8. |
- 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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| 10. |
- Hansbo, Peter F G, 1959, et al.
(författare)
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Energy norm a posteriori error estimates for discontinuous Galerkin approximations of the linear elasticity problem
- 2011
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - Amsterdam : Elsevier BV. - 0045-7825 .- 1879-2138. ; 200:45-46, s. 3026-3030
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Tidskriftsartikel (refereegranskat)abstract
- We present a residual-based a posteriori error estimate in an energy norm of the error in a family of discontinuous Galerkin approximations of linear elasticity problems. The theory is developed in two and three spatial dimensions and general nonconvex polygonal domains are allowed. We also present some illustrating numerical examples.
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