BV Solutions of the Semidiscrete Upwind Scheme
BV Solutions of the Semidiscrete Upwind Scheme
复制标题
半离散迎风方案的BV解
DOI：
10.1007/s00205-002-0237-2
复制
发表时间：
2003
影响因子：
2.5
通讯作者：
S. Bianchini
中科院分区：
文献类型：
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作者：
S. Bianchini
我们考虑半离散迎风格式，证明了：如果（1）的初始数据具有小的全变差，则解u ∈（t）具有一致有界的BV范数，且与t，u ∈无关.此外，通过研究方程（1）的扰动，我们证明了Lipschitz连续依赖于初始数据的u（t）。利用类似于消失粘性情形的技巧，我们证明了当ε →0时，解u ε（t）收敛到相应双曲型方程组的弱解，并且这个弱解与Riemann半群的轨线重合，这是由Liu的Riemann解推广到一般双曲型方程组唯一确定的.
We consider the semidiscrete upwind scheme We prove that if the initial data ū of (1) has small total variation, then the solution uɛ(t) has uniformly bounded BV norm, independent of t, ɛ. Moreover by studying the equation for a perturbation of (1) we prove the Lipschitz-continuous dependence of uɛ(t) on the initial data. Using a technique similar to the vanishing-viscosity case, we show that as ɛ→0 the solution uɛ(t) converges to a weak solution of the corresponding hyperbolic system, Moreover this weak solution coincides with the trajectory of a Riemann semigroup, which is uniquely determined by the extension of Liu's Riemann solver to general hyperbolic systems.