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  • 1.
    Becker, Roland
    et al.
    Université de Pau et des Pays de l'Adour.
    Hansbo, Peter
    Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
    A simple pressure stabilization method for the Stokes equation2008In: Communications in Numerical Methods in Engineering, ISSN 1069-8299, E-ISSN 1099-0887, Vol. 24, no 11, p. 1421-1430Article in journal (Refereed)
    Abstract [en]

    In this paper, we consider a stabilization method for the Stokes problem, using equal-order interpolation of the pressure and velocity, which avoids the use of the mesh size parameter in the stabilization term. We show that our approach is stable for equal-order interpolation in the case of piecewise linear and piecewise quadratic polynomials on triangles. In the case of linear polynomials, we retrieve a well-known idea of using mass lumping as a stabilization mechanism.

  • 2.
    Hansbo, Peter
    Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
    A note on energy conservation for Hamiltonian systems using continuous time finite elements2001In: Communications in Numerical Methods in Engineering, ISSN 1069-8299, E-ISSN 1099-0887, Vol. 17, no 12, p. 863-869Article in journal (Refereed)
    Abstract [en]

    In this note we suggest a now approach to ensure energy conservation in time-continuous finite element methods for non-linear Hamiltonian problems.

  • 3.
    Hansbo, Peter
    Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
    Generalized Laplacian smoothing of unstructured grids1995In: Communications in Numerical Methods in Engineering, ISSN 1069-8299, E-ISSN 1099-0887, Vol. 11, no 5, p. 455-464Article in journal (Refereed)
    Abstract [en]

    In this note we point out the natural choice of smoothing by use of a metric tenser to maintain control of the local element stretch. The extension to grids on surfaces in 3D is straightforward. Numerical examples are given.

  • 4.
    Hansbo, Peter
    Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
    Space-time oriented streamline diffusion methods for nonlinear conservation laws in one dimension1994In: Communications in Numerical Methods in Engineering, ISSN 1069-8299, E-ISSN 1099-0887, Vol. 10, no 3, p. 203-215Article in journal (Refereed)
    Abstract [en]

    In this paper we consider an explicit finite-element method, with elements adaptively oriented in space-time, for the solution of one-dimensional conservation laws, extending previous work dealing with linear convection-diffusion and incompressible flow. In particular we consider Burgers' equation and the compressible Euler equations.

  • 5.
    Hansbo, Peter
    et al.
    Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
    Larson, Mats G.
    Umeå University.
    Piecewise divergence-free discontinuous Galerkin methods for Stokes flow2008In: Communications in Numerical Methods in Engineering, ISSN 1069-8299, E-ISSN 1099-0887, Vol. 24, no 5, p. 355-366Article in journal (Refereed)
    Abstract [en]

    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 C-0 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.

  • 6.
    Hermansson, Joakim
    et al.
    Chalmers University of Technology.
    Hansbo, Peter
    Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
    A variable diffusion method for mesh smoothing2003In: Communications in Numerical Methods in Engineering, ISSN 1069-8299, E-ISSN 1099-0887, Vol. 19, no 11, p. 897-908Article in journal (Refereed)
    Abstract [en]

    In this note we suggest a new approach to mesh smoothing, based on a combination of Laplacian smoothing and Winslow's method. Using our approach, we can avoid mesh folding and maintain/produce element stretch. We also make a comparison with a method due to Giuliani and show that the latter method cannot ensure that folding is avoided.

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