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