论文标题
显式和有效的误差估计凸最小化问题
Explicit and efficient error estimation for convex minimization problems
论文作者
论文摘要
我们结合了一种系统的方法，用于导出一般的后验误差估计，用于基于凸双重关系与最近衍生的广义Marini公式的凸最小化问题的后验错误估计。 A后验误差估计基本上是无恒定的，并且适用于大量的变异问题，包括$ p $ -dirichlet问题，以及退化的最小化，障碍和图像脱落问题。另外，这些后验误差估计基于与给定的不合格元素解决方案的比较。对于$ p $ -Dirichlet问题，这些后验错误界限等于残留的A型后验错误界限，因此，可靠且有效。
We combine a systematic approach for deriving general a posteriori error estimates for convex minimization problems based on convex duality relations with a recently derived generalized Marini formula. The a posteriori error estimates are essentially constant-free and apply to a large class of variational problems including the $p$-Dirichlet problem, as well as degenerate minimization, obstacle and image de-noising problems. In addition, these a posteriori error estimates are based on a comparison to a given non-conforming finite element solution. For the $p$-Dirichlet problem, these a posteriori error bounds are equivalent to residual type a posteriori error bounds and, hence, reliable and efficient.
