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