000			04928nam a22005417a 4500
001			sulb-eb0026127
003			BD-SySUS
005			20160413122610.0
007			cr nn 008mamaa
008			130331s2013 it | s |||| 0|eng d
020			_a9788847028920 _9978-88-470-2892-0
024	7		_a10.1007/978-88-470-2892-0 _2doi
050		4	_aQA71-90
072		7	_aPBKS _2bicssc
072		7	_aMAT006000 _2bisacsh
082	0	4	_a518 _223
100	1		_aGosse, Laurent. _eauthor.
245	1	0	_aComputing Qualitatively Correct Approximations of Balance Laws _h[electronic resource] : _bExponential-Fit, Well-Balanced and Asymptotic-Preserving / _cby Laurent Gosse.
264		1	_aMilano : _bSpringer Milan : _bImprint: Springer, _c2013.
300			_aXIX, 340 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aSIMAI Springer Series, _x2280-840X ; _v2
505	0		_aIntroduction 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.
520			_aSubstantial 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 hyperbolic systems of conservation laws, or simply inhomogeneous scalar balance laws involving accretive or space-dependent source terms, because of complex wave interactions. An overall weaker dissipation can reveal intrinsic numerical weaknesses through specific nonlinear mechanisms: Hugoniot curves being deformed by local averaging steps in Godunov-type schemes, low-order errors propagating along expanding characteristics after having hit a discontinuity, exponential amplification of truncation errors in the presence of accretive source terms... This book aims at presenting rigorous derivations of different, sometimes called well-balanced, numerical schemes which succeed in reconciling high accuracy with a stronger robustness even in the aforementioned accretive contexts. It is divided into two parts: one dealing with hyperbolic systems of balance laws, such as arising from quasi-one dimensional nozzle flow computations, multiphase WKB approximation of linear Schrödinger equations, or gravitational Navier-Stokes systems. Stability results for viscosity solutions of onedimensional balance laws are sketched. The other being entirely devoted to the treatment of weakly nonlinear kinetic equations in the discrete ordinate approximation, such as the ones of radiative transfer, chemotaxis dynamics, semiconductor conduction, spray dynamics of linearized Boltzmann models. “Caseology” is one of the main techniques used in these derivations. Lagrangian techniques for filtration equations are evoked too. Two-dimensional methods are studied in the context of non-degenerate semiconductor models.
650		0	_aMathematics.
650		0	_aPartial differential equations.
650		0	_aApplied mathematics.
650		0	_aEngineering mathematics.
650		0	_aComputer mathematics.
650		0	_aPhysics.
650	1	4	_aMathematics.
650	2	4	_aComputational Mathematics and Numerical Analysis.
650	2	4	_aPartial Differential Equations.
650	2	4	_aApplications of Mathematics.
650	2	4	_aAppl.Mathematics/Computational Methods of Engineering.
650	2	4	_aNumerical and Computational Physics.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9788847028913
830		0	_aSIMAI Springer Series, _x2280-840X ; _v2
856	4	0	_uhttp://dx.doi.org/10.1007/978-88-470-2892-0
912			_aZDB-2-SMA
942			_2Dewey Decimal Classification _ceBooks
999			_c48219 _d48219