| 6141. |
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| 6142. |
- Hansbo, Peter, et al.
(författare)
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Least-squares stabilized augmented Lagrangian multiplier method for elastic contact
- 2016
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Ingår i: Finite elements in analysis and design (Print). - : Elsevier. - 0168-874X .- 1872-6925. ; 116, s. 32-37
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we propose a stabilized augmented Lagrange multiplier method for the finite element solution of small deformation elastic contact problems. We limit ourselves to friction-free contact with a rigid obstacle, but the formulation is readily extendable to more complex situations. © 2016 Elsevier B.V.
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| 6143. |
- Hansbo, Peter, et al.
(författare)
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Locking free quadrilateral continuous/discontinuous finite element methods for the Reissner–Mindlin plate
- 2014
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825 .- 1879-2138. ; 269, s. 381-393
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Tidskriftsartikel (refereegranskat)abstract
- We develop a finite element method with continuous displacements and discontinuous rotations for the Reissner-Mindlin plate model on quadrilateral elements. To avoid shear locking, the rotations must have the same polynomial degree in the parametric reference plane as the parametric derivatives of the displacements, and obey the same transforma- tion law to the physical plane as the gradient of displacements. We prove optimal conver- gence, uniformly in the plate thickness, and provide numerical results that confirm our estimates.
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| 6144. |
- Hansbo, Peter
(författare)
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Moving finite element methods by use of space-time elements : I. Scalar problems
- 1998
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Ingår i: Numerical Methods for Partial Differential Equations. - 0749-159X .- 1098-2426. ; 14:2, s. 251-262
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Tidskriftsartikel (refereegranskat)abstract
- This article deals with moving finite element methods by use of the time-discontinuous Galerkin formulation in combination with oriented space-time meshes. A principle for mesh orientation in space-time based on minimization of the residual, related to adaptive error control via an a posteriori error estimate, is presented. The relation to Miller's moving finite element method is discussed. The article deals with scalar problems: systems will be treated in a companion article.
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| 6145. |
- Hansbo, Peter, et al.
(författare)
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Nitsche's finite element method for model coupling in elasticity
- 2022
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier. - 0045-7825 .- 1879-2138. ; 392
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Tidskriftsartikel (refereegranskat)abstract
- We develop a hybridized Nitsche finite element method for a two dimensional elastic interface problems. Our approach allows for modelling of Euler–Bernoulli beams with axial stiffness embedded in an elastic bulk domain. The beams have their own displacement fields, and the elastic subdomains created by the beam network are triangulated independently and are coupled to the beams weakly by use of Nitsche's method.
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| 6146. |
- Hansbo, Peter, et al.
(författare)
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Nitsche's method combined with space-time finite elements for ALE fluid-structure interaction problems
- 2004
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825 .- 1879-2138. ; 193:39-41, s. 4195-4206
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Tidskriftsartikel (refereegranskat)abstract
- We propose a weak method for handling the fluid-structure interface in finite element fluid-structure interaction based on Nitsche's method [Abh. Math. Univ. Hamburg 36 (1971) 9]. We assume transient incompressible Newtonian flow and, for the structure, undamped linear elasticity. For the time-discretization, we use the time-continuous (energy conserving) Galerkin method for the structure, and for the fluid we employ the time-discontinuous Galerkin method. This means that the velocity becomes piecewise constant on each timestep for the fluid, matching the time-derivative of the displacements in the solid which is also piecewise constant over a time step. We formulate the method and report some numerical examples using space-time oriented elements for the fluid in order to mimic Lagrangian or ALE-type simulations.
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| 6147. |
- Hansbo, Peter, et al.
(författare)
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Nitsche's method for coupling non-matching meshes in fluid-structure vibration problems
- 2003
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Ingår i: Computational Mechanics. - : Springer Science and Business Media LLC. - 0178-7675 .- 1432-0924. ; 32:1-2, s. 134-139
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Tidskriftsartikel (refereegranskat)abstract
- Nitsche's method [11] is a classical method for imposing essential boundary conditions weakly. Unlike the penalty method, it is consistent with the original differential equation. The strong point of Nitsche's method is that it retains the convergence rate of the underlying finite element method, whereas the standard penalty method either requires a "very large" penalty parameter, destroying the condition number of the resulting matrix problem, or, in case the condition number is to be retained, is limited to first order energy-norm accuracy. In this paper, we give a formulation of Nitsche's method suitable for the problem of fluid-structure interaction. Numerical examples are given.
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| 6148. |
- Hansbo, Peter
(författare)
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Nonconforming rotated Q1 tetrahedral element with explicit time stepping for elastodynamics
- 2012
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Ingår i: International Journal for Numerical Methods in Engineering. - : John Wiley & Sons. - 0029-5981 .- 1097-0207. ; 91:10, s. 1105-1114
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we apply a rotated bilinear tetrahedral element to elastodynamics in R3. This element performs superior to the constant strain element in bending and, unlike the conforming linear strain tetrahedron, allows for row-sum lumping of the mass matrix. We study the effect of different choices of approximation (point- wise continuity versus edge average continuity) as well as lumping versus consistent mass in the setting of eigenvibrations. We also use the element in combination with the leapfrog method for time domain com- putations and make numerical comparisons with the constant strain and linear strain tetrahedra.
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| 6149. |
- Hansbo, Peter, et al.
(författare)
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Piecewise divergence-free discontinuous Galerkin methods for Stokes flow
- 2007
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Ingår i: Communications in Numerical Methods in Engineering. - : John Wiley & Sons. - 1069-8299 .- 1099-0887. ; 24:5, s. 355-366
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we consider different possibilities of using divergence‐free discontinuous Galerkin methods for the Stokes problem in order to eliminate the pressure from the discrete problem. We focus on three different approaches: one based on a C0 approximation of the stream function in two dimensions (the vector potential in three dimensions), one based on the non‐conforming Morley element (which corresponds to a divergence‐free non‐conforming Crouzeix–Raviart approximation of the velocities), and one fully discontinuous Galerkin method with a stabilization of the pressure that allows the edgewise elimination of the pressure variable before solving the discrete system. We limit the analysis in the stream function case to two spatial dimensions, while the analysis of the fully discontinuous approach is valid also in three dimensions.
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| 6150. |
- Hansbo, Peter, et al.
(författare)
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STABILIZED FINITE ELEMENT APPROXIMATION OF THE MEAN CURVATURE VECTOR ON CLOSED SURFACES
- 2015
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Ingår i: SIAM Journal on Numerical Analysis. - : Society for Industrial and Applied Mathematics. - 0036-1429 .- 1095-7170. ; 53:4, s. 1806-1832
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Tidskriftsartikel (refereegranskat)abstract
- The mean curvature vector of a surface is obtained by letting the Laplace-Beltrami operator act on the embedding of the surface in R-3. In this contribution we develop a stabilized finite element approximation of the mean curvature vector of certain piecewise linear surfaces which enjoys first order convergence in L-2. The stabilization involves the jump in the tangent gradient in the direction of the outer co-normals at each edge in the surface mesh. We consider both standard meshed surfaces and so-called cut surfaces that are level sets of piecewise linear distance functions. We prove a priori error estimates and verify the theoretical results numerically.
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