Two A Posteriori Error Estimates for One-Dimensional Scalar Conservation Laws
Two A Posteriori Error Estimates for One-Dimensional Scalar Conservation Laws
复制标题
一维标量守恒定律的两个后验误差估计
DOI：
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发表时间：
2000
影响因子：
2.9
通讯作者：
C. Makridakis
中科院分区：
文献类型：
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作者：
L. Gosse;C. Makridakis
本文提出了一维标量守恒律下数值格式的后验局部误差估计。我们首先考虑可以导出一致胞内熵不等式的方案。然后将此结果推广到满足弱熵不等式的二阶粘性格式。为了说明这一点，我们对Burgers方程进行了几个数值测试，并提出了一种自适应网格选择算法。
In this paper, we propose a posteriori local error estimates for numerical schemes in the context of one-dimensional scalar conservation laws. We first consider the schemes for which a consistent in-cell entropy inequality can be derived. Then we extend this result to second-order schemes written in viscous form satisfying weak entropy inequalities. As an illustration, we show several numerical tests on the Burgers equation and we propose an adaptive algorithm for the selection of the mesh.