The SERENA team is concerned with numerical methods for environmental problems. The methods and areas of application are:
Methods
- Conception and analysis of models based on partial differential equations
- Model coupling
- Numerical methods
- Finite element, finite volume, mixed finite element, and discontinuous Galerkin methods
- Structure-preserving numerical discretizations, polygonal and polyhedral meshes
- Discrete geometry
- Solvers
- Domain decomposition
- Newton–Krylov and Newton–multigrid nonlinear algebraic solvers
- A posteriori error estimates, adaptivity, efficiency
- Functional programming and formal proofs for scientific computing
- Reliability (guaranteed error bound) of the overall numerical simulation process
Applications
- Multiphase flows and transport of contaminants in the subsurface
- fractured and porous media
- subsurface depollution after chemical leakage
- nuclear waste disposal in deep underground repositories
- geological sequestration of CO2
- Complex Stokes and Navier–Stokes flows
- Energy production, sustainable use of resources
- shock waves impinging on deformable or fragmentable structures
