论文标题
具有粗糙系数的对流扩散方程的有限体积方案的错误估计值
Error estimates for a finite volume scheme for advection-diffusion equations with rough coefficients
论文作者
论文摘要
我们研究了隐式上风有限体积方案，用于在低规律性diperna-lions设置中用矢量场在数值上近似的对流扩散方程。也就是说，我们关注的是，在空间上是sobolev常规和仅能集成的数据的速度场。我们研究了隐式上风有限体积方案，用于在低规律性diperna-lions设置中用矢量场在数值上近似的对流扩散方程。我们证明，在非结构化的常规网格上，上风方案对连续模型的唯一解决方案产生的近似解决方案的收敛速率至少是一个。数值误差是根据对数Kantorovich-Rubinstein距离估计的，因此提供了弱收敛速率的结合。
We study the implicit upwind finite volume scheme for numerically approximating the advection-diffusion equation with a vector field in the low regularity DiPerna-Lions setting. That is, we are concerned with advecting velocity fields that are spatially Sobolev regular and data that are merely integrable. We study the implicit upwind finite volume scheme for numerically approximating the advection-diffusion equation with a vector field in the low regularity DiPerna-Lions setting. We prove that on unstructured regular meshes the rate of convergence of approximate solutions generated by the upwind scheme towards the unique solution of the continuous model is at least one. The numerical error is estimated in terms of logarithmic Kantorovich-Rubinstein distances and provides thus a bound on the rate of weak convergence.
