A Posteriori Error Estimate for Front-Tracking: Systems of Conservation Laws
A Posteriori Error Estimate for Front-Tracking: Systems of Conservation Laws
复制标题
前沿追踪的后验误差估计：守恒定律系统
DOI：
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发表时间：
2004
影响因子：
2
通讯作者：
M. Laforest
中科院分区：
文献类型：
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作者：
M. Laforest
本文证明了非线性守恒律双曲型方程组的前沿跟踪近似解在L1范数下的后验误差估计。从Bressan，Liu和Yang的L1稳定性结果开始，我们使用他们的L1等价泛函对前跟踪近似，并确定了领先阶对数值误差的贡献。我们的测量误差明确识别的本地来源的误差内的前端跟踪近似。我们还证明了这些局部误差估计是全局误差估计的充要条件。我们将估计应用到一个新的和更广泛的一类前跟踪近似，其中包括Risebro的近似。
We demonstrate an a posteriori error estimate in the L1 norm for front-tracking approximate solutions to hyperbolic systems of nonlinear conservation laws. Starting with the L1 -stability result of Bressan, Liu, and Yang, we use their L1 -equivalent functional for pairs of front-tracking approximations and identify the leading order contribution to the numerical error. Our measure for the error explicitly identifies the local sources of errors within front-tracking approximations. We also show that these local error estimators are necessary and sufficient global error estimators. We apply the estimate to a new and wider class of front-tracking approximations, which includes the approximations of Risebro.