On the stability of finite element methods for shock waves

• 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 [19], 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+ )

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