标题： 一类完全非线性椭圆PDE的最小残差离散化 显示英文标题

标题： Minimal residual discretization of a class of fully nonlinear elliptic PDE

摘要： 这项工作介绍了针对一类椭圆完全非线性偏微分方程的有限元方法。 它们基于一种最小残差原理，该原理建立在Alexandrov--Bakelman--Pucci估计之上。 在对算子的相当一般的结构假设下，证明了$C^1$相容和不连续Galerkin方法在$L^\infty$范数下的收敛性。 提供了在二维和三维空间中，由残差局部信息驱动的自适应网格加密性能的数值实验。 显示英文摘要

摘要： This work introduces finite element methods for a class of elliptic fully nonlinear partial differential equations. They are based on a minimal residual principle that builds upon the Alexandrov--Bakelman--Pucci estimate. Under rather general structural assumptions on the operator, convergence of $C^1$ conforming and discontinuous Galerkin methods is proven in the $L^\infty$ norm. Numerical experiments on the performance of adaptive mesh refinement driven by local information of the residual in two and three space dimensions are provided.