TY - JOUR
T1 - A new Glimm functional and convergence rate of Glimm scheme for general systems of hyperbolic conservation laws
AU - Hua, Jiale
AU - Jiang, Zaihong
AU - Yang, Tong
PY - 2010/5
Y1 - 2010/5
N2 - In this paper, we introduce a new Glimm functional for general systems of hyperbolic conservation laws. This new functional is consistent with the classical Glimm functional for the case when each characteristic field is either genuinely nonlinear or linearly degenerate, so that it can be viewed as "optimal" in some sense. With this new functional, the consistency of the Glimm scheme is proved clearly for general systems. Moreover, the convergence rate of the Glimm scheme is shown to be the same as the one obtained in Bressan, Marson (Arch Ration Mech Anal 142(2):155-176, 1998) for systems with each characteristic field being genuinely nonlinear or linearly degenerate. © Springer-Verlag 2009.
AB - In this paper, we introduce a new Glimm functional for general systems of hyperbolic conservation laws. This new functional is consistent with the classical Glimm functional for the case when each characteristic field is either genuinely nonlinear or linearly degenerate, so that it can be viewed as "optimal" in some sense. With this new functional, the consistency of the Glimm scheme is proved clearly for general systems. Moreover, the convergence rate of the Glimm scheme is shown to be the same as the one obtained in Bressan, Marson (Arch Ration Mech Anal 142(2):155-176, 1998) for systems with each characteristic field being genuinely nonlinear or linearly degenerate. © Springer-Verlag 2009.
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U2 - 10.1007/s00205-009-0266-1
DO - 10.1007/s00205-009-0266-1
M3 - RGC 21 - Publication in refereed journal
SN - 0003-9527
VL - 196
SP - 433
EP - 454
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
IS - 2
ER -