Computing Qualitatively Correct Approximations of Balance Laws Exponential-Fit, Well-Balanced and Asymptotic-Preserving /
Substantial effort has been drawn for years onto the development of (possibly high-order) numerical techniques for the scalar homogeneous conservation law, an equation which is strongly dissipative in L1 thanks to shock wave formation. Such a dissipation property is generally lost when considering h...
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| Language: | English |
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Milano :
Springer Milan : Imprint: Springer,
2013.
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| Edition: | 1st ed. 2013. |
| Series: | SEMA SIMAI Springer Series,
2 |
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| Online Access: | https://doi.org/10.1007/978-88-470-2892-0 |
Table of Contents:
- 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.