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