@Article{CiCP-31-5,
author = {Yong, Yang and Wenrui, Hao and Zhang, Yong-Tao},
title = {A Continuous Finite Element Method with Homotopy Vanishing Viscosity for Solving the Static Eikonal Equation},
journal = {Communications in Computational Physics},
year = {2022},
volume = {31},
number = {5},
pages = {1402--1433},
abstract = {<p style="text-align: justify;">We develop a second-order continuous finite element method for solving
the static Eikonal equation. It is based on the vanishing viscosity approach with a homotopy method for solving the discretized nonlinear system. More specifically, the homotopy method is utilized to decrease the viscosity coefficient gradually, while Newton’s method is applied to compute the solution for each viscosity coefficient. Newton’s method alone converges for just big enough viscosity coefficients on very coarse
grids and for simple 1D examples, but the proposed method is much more robust and
guarantees the convergence of the nonlinear solver for all viscosity coefficients and for
all examples over all grids. Numerical experiments from 1D to 3D are presented to
confirm the second-order convergence and the effectiveness of the proposed method
on both structured or unstructured meshes.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2021-0164},
url = {https://global-sci.com/article/79551/a-continuous-finite-element-method-with-homotopy-vanishing-viscosity-for-solving-the-static-eikonal-equation}
}