Two-scale method for the Monge–Ampère equation: pointwise error estimates
Two-scale method for the Monge–Ampère equation: pointwise error estimates
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Monge–Ampère 方程的二尺度方法：逐点误差估计
DOI：
10.1093/imanum/dry026
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发表时间：
2018
影响因子：
2.1
通讯作者：
Zhang, W
中科院分区：
文献类型：
--
作者：
Nochetto, R H;Ntogkas, D;Zhang, W
本文继续分析了Nochettoet等人在研究中提出的求解维数≥ 2的Monge-Ampère方程的双尺度方法。(2017，Monge-Ampère方程的双尺度方法：收敛于粘性解。数学计算，印刷中）。我们证明了连续依赖的离散解决方案的数据，反过来又取决于一个离散版本的Alexandroff估计。他们都是工具，以证明逐点误差估计的经典解决方案与Hölder和Sobolev正则性。我们还得到了收敛速度的粘性解有界海森，这可能是分段光滑或退化。
In this paper we continue the analysis of the two-scale method for the Monge–Ampère equation for dimensiond≥ 2 introduced in the study by Nochettoet al.(2017, Two-scale method for the Monge–Ampère equation: convergence to the viscosity solution.Math. Comput., in press). We prove continuous dependence of discrete solutions on data that in turn hinges on a discrete version of the Alexandroff estimate. They are both instrumental to prove pointwise error estimates for classical solutions with Hölder and Sobolev regularity. We also derive convergence rates for viscosity solutions with bounded Hessians which may be piecewise smooth or degenerate.