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