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