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# Computing Qualitatively Correct Approximations of Balance Laws

## Exponential-Fit, Well-Balanced and Asymptotic-Preserving

Surveys both analytical and numerical aspects of hyperbolic balance laws (including the recent theory of viscosity solutions for systems)

Numerous derivations of both well-balanced and asymptotic-preserving schemes emphasizing relations between each other Includes original material about K-multibranch solutions for linear geometric optics or order-preserving strings

Several chapters about numerical approximation of chemotaxis or semiconductor kinetic models which display constant macroscopic fluxes at stationary state ("qualitatively correct" approximations)

Presents well-balanced techniques for linearized Boltzmann and Fokker-Planck kinetic equations

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Part of the SIMAI Springer Series book series (SEMA SIMAI, volume 2)