Hypocoercivity Based Sensitivity Analysis and Spectral Convergence of the Stochastic Galerkin Approximation to Collisional Kinetic Equations with Multiple Scales and Random Inputs

DOI10.1137/17M1151730zbMath1403.35197arXiv1710.00226OpenAlexW2963023431MaRDI QIDQ4689142

Liu Liu, Shih Jin

Publication date: 15 October 2018

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.00226

zbMATH Keywords

sensitivity analysismultiple scaleshypocoercivitykinetic equations with uncertaintiesgPC stochastic Galerkin

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Navier-Stokes equations for incompressible viscous fluids (76D05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) PDEs with randomness, stochastic partial differential equations (35R60) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Kinetic theory of gases in equilibrium statistical mechanics (82B40) Boltzmann equations (35Q20)

Related Items (21)

Monte Carlo stochastic Galerkin methods for the Boltzmann equation with uncertainties: space-homogeneous case ⋮ Asymptotic-preserving schemes for multiscale physical problems ⋮ A stochastic kinetic scheme for multi-scale plasma transport with uncertainty quantification ⋮ A local sensitivity analysis for the kinetic Cucker-Smale equation with random inputs ⋮ On the multi-species Boltzmann equation with uncertainty and its stochastic Galerkin approximation ⋮ Monte Carlo stochastic Galerkin methods for non-Maxwellian kinetic models of multiagent systems with uncertainties ⋮ A study of Landau damping with random initial inputs ⋮ Local Sensitivity Analysis for the Kuramoto--Daido Model with Random Inputs in a Large Coupling Regime ⋮ A structure and asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck model ⋮ Local sensitivity analysis for the Cucker-Smale model with random inputs ⋮ Multi-scale control variate methods for uncertainty quantification in kinetic equations ⋮ On stochastic Galerkin approximation of the nonlinear Boltzmann equation with uncertainty in the fluid regime ⋮ A bi-fidelity method for the multiscale Boltzmann equation with random parameters ⋮ Hypocoercivity for a BGK model for gas mixtures ⋮ A local sensitivity and regularity analysis for the Vlasov-Poisson-Fokker-Planck system with multi-dimensional uncertainty and the spectral convergence of the stochastic Galerkin method ⋮ Multiscale Variance Reduction Methods Based on Multiple Control Variates for Kinetic Equations with Uncertainties ⋮ Sensitivity analysis of the non-linear Fokker-Planck equations with uncertainty ⋮ A stochastic asymptotic-preserving scheme for the bipolar semiconductor Boltzmann-Poisson system with random inputs and diffusive scalings ⋮ Sharp decay estimates in local sensitivity analysis for evolution equations with uncertainties: from ODEs to linear kinetic equations ⋮ A study of hyperbolicity of kinetic stochastic Galerkin system for the isentropic Euler equations with uncertainty ⋮ The Vlasov-Fokker-Planck equation with high dimensional parametric forcing term

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