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