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