基于局部变分原理的静态Hamilton-Jacobi方程有限元离散
Finite-Element Discretization of Static Hamilton-Jacobi Equations Based on a Local Variational Principle
AI总结：
本文提出一种基于局部变分原理的线性有限元离散方法，用于求解非结构化三角剖分上的静态Hamilton-Jacobi方程Dirichlet问题，并采用自适应Gauss-Seidel迭代高效求解。该方法推广了现有方法并具备简洁的收敛理论。
摘要：
我们针对非结构化三角剖分上的静态Hamilton-Jacobi方程的Dirichlet问题，提出了一种线性有限元离散方法。该离散基于简化的局部Dirichlet问题，并通过局部变分原理求解。它推广了文献中已知的几种方法，并允许简单透明的收敛理论。本文中，所得非线性方程组通过自适应Gauss-Seidel迭代求解，该迭代易于实现且相当有效，数值实验证明了这一点。
英文摘要：
We propose a linear finite-element discretization of Dirichlet problems for static Hamilton-Jacobi equations on unstructured triangulations. The discretization is based on simplified localized Dirichlet problems that are solved by a local variational principle. It generalizes several approaches known in the literature and allows for a simple and transparent convergence theory. In this paper the resulting system of nonlinear equations is solved by an adaptive Gauss-Seidel iteration that is easily implemented and quite effective as a couple of numerical experiments show.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
