论文标题
凸最小化问题和与混合方法的精确关系的不合格离散
Nonconforming discretizations of convex minimization problems and precise relations to mixed methods
论文作者
论文摘要
本文讨论了不合格的有限元方法，以最小化问题，并系统地得出双重混合配方。二元关系导致简单的错误估计，避免了对非符号错误的明确处理。重建公式通过简单的后处理过程提供了双重问题的离散解决方案，该过程意味着强大的二元性关系，并且在后验误差估计中很感兴趣。该框架适用于可区分和非平滑的问题，例如$ p $ - laplace，总变化正规化和障碍物问题。数值实验说明了与标准构象法相比不合格的优势。
This article discusses nonconforming finite element methods for convex minimization problems and systematically derives dual mixed formulations. Duality relations lead to simple error estimates that avoid an explicit treatment of nonconformity errors. A reconstruction formula provides the discrete solution of the dual problem via a simple postprocessing procedure which implies a strong duality relation and is of interest in a posteriori error estimation. The framework applies to differentiable and nonsmooth problems, examples include $p$-Laplace, total-variation regularized, and obstacle problems. Numerical experiments illustrate advantages of nonconforming over standard conforming methods.
