| 1. |
- 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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| 2. |
- 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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| 3. |
- 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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| 4. |
- Hansbo, Peter F G, 1959, et al.
(författare)
-
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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| 5. |
- Becker, R., et al.
(författare)
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A finite element time relaxation method
- 2011
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Ingår i: Comptes Rendus Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 349:5-6, s. 353-356
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Tidskriftsartikel (refereegranskat)abstract
- We discuss a finite element time-relaxation method for high Reynolds number flows. The method uses local projections on polynomials defined on macroelements of each pair of two elements sharing a face. We prove that this method shares the optimal stability and convergence properties of the continuous interior penalty (CIP) method. We give the formulation both for the scalar convection-diffusion equation and the time-dependent incompressible Euler equations and the associated convergence results. This note finishes with some numerical illustrations. (C) 2010 Academic des sciences. Published by Elsevier Masson SAS. All rights reserved.
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| 6. |
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| 7. |
- Chernov, A.V., et al.
(författare)
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An hp-Nitsche's method for interface problems with nonconforming unstructured finite element meshes
- 2011
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Ingår i: Lecture Notes in Computational Science and Engineering: 8th International Conference on Spectral and High Order Methods, ICOSAHOM'09; Trondheim; Norway; 22 June 2009 through 26 June 2009. - Berlin, Heidelberg : Springer Berlin Heidelberg. - 1439-7358 .- 2197-7100. - 9783642153365 ; 76, s. 153-161, s. 153-161
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Konferensbidrag (refereegranskat)abstract
- In this paper we propose an hp-Nitsche's method for the finite element solution of interface elliptic problems using non-matched unstructured meshes of triangles and parallelograms in ℝ2 and tetrahedra and parallelepipeds in ℝ3. We obtain an explicit lower bound for the penalty weighting function in terms of the local inverse inequality constant. We prove a priori error estimates which are explicit in the mesh size h and in the polynomial degree p. The error bound is optimal in h and suboptimal in polynomial degree by p1/2.
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| 8. |
- Hansbo, Peter F G, 1959, et al.
(författare)
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A Lagrange multiplier method for the finite element solution of elliptic interface problems using non–matching meshes
- 2005
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Ingår i: Numerische Mathematik. - : Springer Science and Business Media LLC. - 0029-599X .- 0945-3245. ; 100:1, s. 91-115
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we propose a Lagrange multiplier method for the finite element solution of multi-domain elliptic partial differential equations using non-matching meshes. The interface Lagrange multiplier is chosen with the purpose of avoiding the cumbersome integration of products of functions on unrelated meshes (e.g, we will consider global polynomials as multiplier). 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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| 9. |
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| 10. |
- Hansbo, Peter F G, 1959
(författare)
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Three lectures on error estimation and adaptivity
- 2005
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Ingår i: Adaptive Finite Elements in Linear and Nonlinear Solid and Structural Mechanics. - Vienna : Springer Vienna. - 9783211269756 ; , s. 149-193
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- In the first Section, we consider global control of the discretization error in time and space-time using finite element methods in both space and time. The approach we use gives the opportunity for adaptive control of general functionals based on residualtype a posteriori error estimates. In the second Section we apply the general theory to model problems in elasto-plasticity. We consider both the Hencky total deformation theory and the Prandtl-Reuss quasi-static theory, including load step control. Finally, in the third Section, we review some standard techniques for generating meshes, and for handling local mesh refinement.
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