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Finite Element Method (FEM)

SINTEF has a strong competence in Finite Element Methods (FEM). FEM is widely used methods for solving problems in science and engineering. In particular, FEM is a popular method for numerical solution of partial differential equations. We in SINTEF has experiences with developing object oriented adaptive and parallel software modules applicable for computational mechanics. This includes solid/structural and fluid mechanics relevant for civil, mechanical, marine and petroleum engineering as well as biomechanics, geophysics and renewable energy.

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We have made innovative contributions to the following FEM-technologies:

  • Adaptive FEM based on a posteriori error estimates
  • Coupled problems (e.g. fluid-structure interaction)
  • Isogeometric analysis (using splines as basis functions)
  • Reduced order modelling

We have developed an open source objectoriented adaptive parallel isogeometric FEM-module denoted IFEM (Isogeometric Finite Element Module) which has been applied to the following applications:

  • 1D, 2D and 3D linear and non-linear solid mechanics
  • Beam, membrane, plates and shell structural mechanics
  • Poisson problems e.g. heat equation
  • Advection diffusion problems
  • 2D and 3D Stokes problems
  • 2D and 3D (including high Reynolds flow) Navier-Stokes problems
  • 2D and 3D Boussinesq equations
  • Porous media flow
  • Coupled problems:
    • Thermoelasticity
    • Poroelasticity
    • Fluid-structure interaction

We can combine our high-fidelity FEM-models with Reduced Order Modelling (ROM) which is a promising technique to deliver numerical solutions of parametrized PDEs in real-time with reasonable accuracy.