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| 3. |
- Becker, Roland, et al.
(författare)
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Energy norm a posteriori error estimation for discontinuous Galerkin methods
- 2003
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - 0045-7825 .- 1879-2138. ; 192:5-6, s. 723-733
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we present a residual-based a posteriori error estimate of a natural mesh dependent energy norm of the error in a family of discontinuous Galerkin approximations of elliptic problems. The theory is developed for an elliptic model problem 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. |
- Hansbo, Anita, 1960-, et al.
(författare)
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A finite element method on composite grids based on Nitsche's method
- 2003
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Ingår i: Mathematical Modelling and Numerical Analysis. - : EDP Sciences. - 0764-583X .- 1290-3841. ; 37:3, s. 495-514
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we propose a finite element method for the approximation of second order elliptic problems on composite grids. The method is based on continuous piecewise polynomial approximation on each grid and weak enforcement of the proper continuity at an artificial interface defined by edges (or faces) of one the grids. We prove optimal order a priori and energy type a posteriori error estimates in 2 and 3 space dimensions, and present some numerical examples.
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| 7. |
- Hansbo, Peter, et al.
(författare)
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A simple nonconforming bilinear element for the elasticity problem
- 2001
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Ingår i: Trends in computational structural mechanics. - BARCELONA : INT CENTER NUMERICAL METHODS ENGINEERING. - 9788489925779 ; , s. 317-327
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- We look at the mixed non-conforming Rannacher-Turek (RT) element from the point of view of discontinuous Galerkin methods. In the case of the elasticity operator, for which the RT element is not stable in that it does not (in general) fulfill a discrete horn's inequality, the discontinuous framework naturally suggests the appearance of (weakly consistent) stabilization terms. We thus obtain a modifed, stable and locking free, version of the RT element for the elasticity problem. We also give some implementation aspects of the element. Numerical results are included.
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| 8. |
- Hansbo, Peter, et al.
(författare)
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Discontinuous Galerkin and the Crouzeix-Raviart element : Application to elasticity
- 2003
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Ingår i: Mathematical Modelling and Numerical Analysis. - : EDP Sciences. - 0764-583X .- 1290-3841. ; 37:1, s. 63-72
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Tidskriftsartikel (refereegranskat)abstract
- We propose a discontinuous Galerkin method for linear elasticity, based on discontinuous piecewise linear approximation of the displacements. We show optimal order a priori error estimates, uniform in the incompressible limit, and thus locking is avoided. The discontinuous Galerkin method is closely related to the non-conforming Crouzeix-Raviart (CR) element, which in fact is obtained when one of the stabilizing parameters tends to infinity. In the case of the elasticity operator, for which the CR element is not stable in that it does not fulfill a discrete Korn's inequality, the discontinuous framework naturally suggests the appearance of (weakly consistent) stabilization terms. Thus, a stabilized version of the CR element, which does not lock, can be used for both compressible and ( nearly) incompressible elasticity. Numerical results supporting these assertions are included. The analysis directly extends to higher order elements and three spatial dimensions.
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| 9. |
- Hansbo, Peter, et al.
(författare)
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Discontinuous Galerkin methods for incompressible and nearly incompressible elasticity by Nitsche's method
- 2002
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - 0045-7825 .- 1879-2138. ; 191:17-18, s. 1895-1908
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Tidskriftsartikel (refereegranskat)abstract
- We propose and analyze a discontinuous finite element method for nearly incompressible linear elasticity on triangular meshes. We show optimal error estimates that are uniform with respect to Poisson's ratio. The method is thus locking free. We also introduce an equivalent mixed formulation, allowing for completely incompressible elasticity problems. Numerical results are presented.
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| 10. |
- Hansbo, Peter F G, 1959, et al.
(författare)
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A discontinuous Galerkin method for the plate equation
- 2002
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Ingår i: Calcolo. - : Springer Science and Business Media LLC. - 0008-0624 .- 1126-5434. ; 39:1, s. 41-59
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Tidskriftsartikel (refereegranskat)abstract
- We present a discontinuous Galerkin method for the plate problem. The method employs a discontinuous approximation space allowing nonmatching grids and different types of approximation spaces. Continuity is enforced weakly through the variational form. Discrete approximations of the normal and twisting moments and the transversal force, which satisfy the equilibrium condition on an element level, occur naturally in the method. We show optimal a priori error estimates in various norms and investigate locking phenomena when certain stabilization parameters tend to infinity. Finally, we relate the method to two classical elements: the nonconforming Morley element and the C^1 Argyris element.
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