Computing Qualitatively Correct Approximations of Balance Laws: Exponential-Fit, Well-Balanced and Asymptotic-Preserving - Softcover

Inhaltsangabe

Introduction and chronological perspective.- Lifting a non-resonant scalar balance law.- Lyapunov functional for linear error estimates.- Early well-balanced derivations for various systems.- Viscosity solutions and large-time behavior for non-resonant balance laws.- Kinetic scheme with reflections and linear geometric optics.- Material variables, strings and infinite domains.- The special case of 2-velocity kinetic models.- Elementary solutions and analytical discrete-ordinates for radiative transfer.- Aggregation phenomena with kinetic models of chemotaxis dynamics.- Time-stabilization on flat currents with non-degenerate Boltzmann-Poisson models.- Klein-Kramers equation and Burgers/Fokker-Planck model of spray.- A model for scattering of forward-peaked beams.- Linearized BGK model of heat transfer.- Balances in two dimensions: kinetic semiconductor equations again.- Non-conservative products and locally Lipschitzian paths.- A tiny step toward hypocoercivity estimates for well-balanced schemes on 2x2 models.- Preliminary analysis of the errors for Vlasov-BGK.

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