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.