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Finite Element Methods (FEM)

Finite Element Methods (FEM) are extensively employed for addressing scientific and engineering issues modeled by partial differential equations (PDEs). Within SINTEF, we specialize in the development of object-oriented adaptive and parallel software tailored for computational mechanics and various other domains. Our proficiency spans solid, structural, and fluid mechanics pertinent to civil, mechanical, marine, and petroleum engineering, alongside biomechanics, geophysics, and renewable energy applications.

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We have made innovative contributions to a wide range of FEM technologies, including

  • Adaptive FEM based on a posteriori error estimates
  • Coupled problems, such as fluid-structure interaction
  • Cut FEM for problems with dynamic domains
  • Isogeometric analysis using splines as basis functions
  • Multiscale mixed FEM for flow in porous media
  • Reduced-order modelling for fast numerical solution of parameterized PDEs
  • Virtual element methods for meshes with general polyhedral elements

As an example, we have developed an open-source object oriented adaptive parallel isogeometric FEM module called IFEM (Isogeometric Finite Element Module) available at, which has been applied to a range of problems:

  • 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 technique for delivering numerical solutions of parametrized PDEs in real-time with reasonable accuracy.

We also have expertise in the FEniCS computing platform ( and proficiency in mesh generation methods and standard software such as Gmsh , or our own UPR module for constrained Voronoi grids.

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