蒙日-安培方程近似值的稳定性和保证误差控制

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
Dietmar Gallistl, Ngoc Tien Tran
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引用次数: 0

摘要

本文通过均匀椭圆哈密顿-雅可比-贝尔曼方程分析了蒙日-安培方程的正则化方案。主要工具是来自粘度解理论的 \(L^\infty \) norm 中的稳定性估计,它与正则化参数 \(\varepsilon \) 无关。它们允许正则化问题的解\(u_\varepsilon \)向任何非负\(L^n\)右边和连续狄利克特数据的蒙日-安培方程的亚历山德罗夫解u均匀收敛。主要应用是保证连续可微有限元近似 u 或 \(u_\varepsilon \)的 \(L^\infty \)规范的后验误差边界。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Stability and guaranteed error control of approximations to the Monge–Ampère equation

Stability and guaranteed error control of approximations to the Monge–Ampère equation

This paper analyzes a regularization scheme of the Monge–Ampère equation by uniformly elliptic Hamilton–Jacobi–Bellman equations. The main tools are stability estimates in the \(L^\infty \) norm from the theory of viscosity solutions which are independent of the regularization parameter \(\varepsilon \). They allow for the uniform convergence of the solution \(u_\varepsilon \) to the regularized problem towards the Alexandrov solution u to the Monge–Ampère equation for any nonnegative \(L^n\) right-hand side and continuous Dirichlet data. The main application are guaranteed a posteriori error bounds in the \(L^\infty \) norm for continuously differentiable finite element approximations of u or \(u_\varepsilon \).

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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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