Monotone split- and unsplit methods for a single conservation law in two space dimensions

SIGLETIB Hannover: RO 8680(57) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

A system of conservation laws with a relaxation term

We consider a 2 x system of conservation laws including a stiff relaxation term. Well-posedness of the system, the rate of convergence to equilibrium, and the rate of convergence for a finite difference scheme is discussed. Also a numerical example is presented. (orig.)Available from TIB Hannover: RN 8680(103) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Finite difference schemes for scalar conservation laws with source terms

SIGLEAvailable from TIB Hannover: RN 8680(107) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Local existence and stability for a hyperbolic-elliptic system modeling two-phase reservoir flow

A system arising in the modeling of oil-recovery processes is analyzed. It consists of a hyperbolic conservation law governing the saturation and a elliptic equation for the pressure. By an operator splitting approach, an approximate solution is constructed. For this approximation appropriate a-priori bounds are derived. Applying the Arzela-Ascoli theorem, local existence and uniqueness of a classical solution for the origonal hyperbolic-elliptic system is proved. Furthermore, convergence of the approximation generated by operator splitting towards the unique solution follows. It is also proved that the unique solution is stable with respect to perturbations of the initial data. (orig.)SIGLEAvailable from TIB Hannover: RN 8680(136) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Stiff well-posedness for hyperbolic systems with large relaxation terms (Linear constant-coefficient problems)

The Cauchy problem for linear constant-coefficient hyperbolic systems u_t + Au_x = (1/#delta#)Bu is analyzed. Here (1/#delta#)Bu is a large relaxation term, and we are mostly interested in the critical case where B has a non-trivial nullspace. A concept of stiff well-posedness is introduced that ensures solution estimates independent of 0 < #delta# #<=# 1. Under suitable assumptions, we prove convergence of the L_2-solution to a limit as #delta# tends to zero. The limit solves a reduced strongly hyperbolic system without zero-order term, the so-called equilibrium system, and we present a method to determine this limit system. For 2 x 2 systems the requirement of stiff well-posedness is shown to be equivalent to the well-known subcharacteristic condition, but in general the subcharacteristic condition is not suffient for stiff well-posedness. The theory is illustrated by examples. (orig.)Available from TIB Hannover: RN 8680(125) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Stiff well-posedness for hyperbolic systems with large relaxation terms (Linear constant-coefficient problems)

The Cauchy problem for linear constant-coefficient hyperbolic systems u_t + Au_x = (1/#delta#)Bu is analyzed. Here (1/#delta#)Bu is a large relaxation term, and we are mostly interested in the critical case where B has a non-trivial nullspace. A concept of stiff well-posedness is introduced that ensures solution estimates independent of 0 < #delta# #<=# 1. Under suitable assumptions, we prove convergence of the L_2-solution to a limit as #delta# tends to zero. The limit solves a reduced strongly hyperbolic system without zero-order term, the so-called equilibrium system, and we present a method to determine this limit system. For 2 x 2 systems the requirement of stiff well-posedness is shown to be equivalent to the well-known subcharacteristic condition, but in general the subcharacteristic condition is not suffient for stiff well-posedness. The theory is illustrated by examples. (orig.)Available from TIB Hannover: RN 8680(125) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman