Averaged Multivalued Solutions for Scalar Conservation Laws
Averaged Multivalued Solutions for Scalar Conservation Laws
复制标题
标量守恒定律的平均多值解
DOI：
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发表时间：
1984
期刊：
影响因子：
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通讯作者：
Y. Brenier
中科院分区：
文献类型：
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作者：
Y. Brenier
时间离散的标量守恒律，其中包括平均（在适当的意义上）的一般多值解的经典方法的特征。证明了该方法收敛于满足熵条件的物理解。几个数值方案推导后，完全离散化，无论是相对于空间变量（各种已知的计划，然后承认），或相对于相变量（这导致一个空间网格自由计划）。广义被认为是向系统的守恒律和二维标量守恒律。
A time discretization is introduced for scalar conservation laws, which consists in averaging (in an appropriate sense) the generally multivalued solution given by the classical method of characteristics. Convergence toward the physical solutions satisfying the entropy condition is proved. Several numerical schemes are deduced after a full discretization, either with respect to the space variable (various known schemes are then recognized), or with respect to the phase variable (which leads to a space grid free scheme). Generalizations are considered toward systems of conservation laws and bidimensional scalar conservation laws.