论文标题
一个狭窄的模具框架，用于完全非线性二阶PDE的收敛数值近似值
A narrow-stencil framework for convergent numerical approximations of fully nonlinear second order PDEs
论文作者
论文摘要
本文开发了一个统一的通用框架，用于设计有限的有限差和不连续的Galerkin方法，用于近似粘度和完全非线性二阶PDE的常规解。与众所周知的单调框架（有限差）框架不同，提出的新框架允许使用狭窄的模板和非结构化网格，这使得可以构建高阶方法。一般框架是基于一致性和G-单调性的概念，这些概念都根据各种数值衍生操作员定义。满足框架的特定方法是使用数值力矩构建的。证明了可接受性，稳定性和收敛性，并提供了一些计算机实现详细信息。
This paper develops a unified general framework for designing convergent finite difference and discontinuous Galerkin methods for approximating viscosity and regular solutions of fully nonlinear second order PDEs. Unlike the well-known monotone (finite difference) framework, the proposed new framework allows for the use of narrow stencils and unstructured grids which makes it possible to construct high order methods. The general framework is based on the concepts of consistency and g-monotonicity which are both defined in terms of various numerical derivative operators. Specific methods that satisfy the framework are constructed using numerical moments. Admissibility, stability, and convergence properties are proved, and numerical experiments are provided along with some computer implementation details.
