Numerical simulations Nonlinear Schrödinger equation Binary alloys Existence Degenerate parabolic equations Numerical range Markov chain Numerical simulation Micro-macro decomposition Navier-Stokes equations Population dynamics Robust control Regularity Schrödinger equation Fractured porous media Viscosity solutions Lower-bound gradient estimate Kinetic equations Uniform accuracy Stability Two-scale convergence FOS Mathematics B-series Backward error analysis Asymptotic behavior Elasticity Averaging Invariant measure Controllability Dislocation dynamics Nonlocal front propagation Error estimate Partial differential equations Convergence BGK equation Entropy Asymptotic preserving schemes PIV Invariant measures Fluid mechanics Diffusion limit Optimal control Nonlocal Hamilton-Jacobi Equations Stroboscopic averaging $L^1-$dependence in time Modal analysis Subdivision Timoshenko beam Vlasov equation Asymptotic analysis Asymptotic Analysis Data assimilation Turbulence Fluid-structure interaction Adjoint model White noise Turbulence models Navier-Stokes Equations Reaction-diffusion Level-set approach Numerical analysis Finite element method Dynamical system Stochastic partial differential equations Conservation laws Chapman-Enskog expansion Deconvolution models Cardiac electrophysiology Eikonal equation Reaction-diffusion system Scattering Ensemble forecasting MPCC Density matrix Uncertainty quantification Homogenization Vlasov-Poisson equation Long-time behavior Diffusion DATA ASSIMILATION Boundary layer Hamilton-Jacobi equations Porous media Conduction Robust optimization Données ouvertes Spectral set Highly oscillatory problems Maximum principle Ensemble forecasts Global existence Interaction fluide-structure 65L20 Concrete Optimization Finite Element Method Oceanography Shape optimization Large eddy simulation Fine-scale substructure