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, discontinuous Galerkin methods
- Hybrid high-order methods, polygonal and polyhedral meshes
- Invariant-domain preserving methods for hyperbolic problems
- Solvers
- Domain decomposition
- A-posteriori-steered p-robust multigrid
- Newton–Krylov and Newton–multigrid nonlinear solvers
- High-order discretization of ill-posed problems related to data assimilation
- Model reduction for variational inequalities and shape variability
- 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
- (In)compressible Stokes and Navier–Stokes flows
- Energy production, sustainable use of resources
- Nonlinear mechanics with contact and friction
- Wave propagation in structures and in geosciences
