具有Panov型间断通量的多维标量守恒律方程的Goddom型格式及其误差估计
A Godunov type scheme and error estimates for multidimensional scalar conservation laws with Panov-type discontinuous flux
摘要：
本文讨论一个标量多维守恒律，其中通量为Panov型，且可能含有空间间断。定义了熵解的概念，证明了熵解的唯一性。我们提出了一个Godunov型有限体积格式，并证明了Godunov近似收敛于熵解，从而建立了熵解的存在性。我们还表明，我们的数值方案收敛在$\mathcal{O}(\sqrt{\D t}).$的最佳速度。据我们所知，收敛的Goddom型方法在多维和误差估计的数值方案在一个以及在几个维度是第一个它的一类不连续通量守恒律。我们提出的数值例子来说明理论。
英文摘要：
This article concerns a scalar multidimensional conservation law where the flux is of Panov type and may contain spatial discontinuities. We define a notion of entropy solution and prove that entropy solutions are unique. We propose a Godunov-type finite volume scheme and prove that the Godunov approximations converge to an entropy solution, thus establishing existence of entropy solutions. We also show that our numerical scheme converges at an optimal rate of $\mathcal{O}(\sqrt{\D t}).$ To the best of our knowledge, convergence of the Godunov type methods in multi-dimension and error estimates of the numerical scheme in one as well as in several dimensions are the first of it's kind for conservation laws with discontinuous flux. We present numerical examples that illustrate the theory.
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