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