On the stability of ﬁnite element methods for shock waves
1992 (English)In: Communications on Pure and Applied Mathematics, ISSN 0010-3640, E-ISSN 1097-0312, Vol. 45, no 8, 923-946 p.Article in journal (Refereed) Published
this paper we study the large time asymptotic stability of solutions for systems of nonlinear viscous conservation laws of the form (1:1) u t + f(u) x = u xx ; x 2 R I ; t ? 0 ; u 2 R I u(\Delta; 0) = u 0 (\Delta) : We treat systems which are strictly hyperbolic. Such systems possess a smooth travelling wave solution, which is called a viscous p-shock wave solution, u(x; t) = OE(x \Gamma oet) x!\Sigma1 OE(x) = u \Sigma ; provided that the shock strength ffl j ju + \Gamma u \Gamma j is small , the constant states u \Sigma and the wave speed oe are related by the Rankine-Hugoniot condition (1:3a) f(u \Gamma ) \Gamma f(u+ ) = oe(u \Gamma \Gamma u+ )
Place, publisher, year, edition, pages
NEW YORK: John Wiley & Sons, 1992. Vol. 45, no 8, 923-946 p.
SCALAR CONSERVATION-LAWS, CONVERGENCE, PROFILES
IdentifiersURN: urn:nbn:se:kth:diva-51565DOI: 10.1002/cpa.3160450802ISI: A1992JH50600001OAI: oai:DiVA.org:kth-51565DiVA: diva2:464621
QC 201112142011-12-132011-12-132012-02-27Bibliographically approved