Modified Two-Grid Algorithm for Nonlinear Power-Law Conductivity in Maxwell's Problems with High Accuracy
Year: 2021
Author: Changhui Yao, Yanfei Li
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 2 : pp. 481–502
Abstract
In this paper, we develop the superconvergence analysis of two-grid algorithm by Crank-Nicolson finite element discrete scheme with the lowest Nédélec element for nonlinear power-law conductivity in Maxwell's problems. Our main contribution will have two parts. On the one hand, in order to overcome the difficulty of misconvergence of classical two-grid method by the lowest Nédélec element, we employ the Newton-type Taylor expansion at the superconvergent solutions for the nonlinear terms on coarse mesh, which is different from the numerical solution on the coarse mesh classically. On the other hand, we push the two-grid solution to high accuracy by the postprocessing interpolation technique. Such a design can improve the computational accuracy in space and decrease time consumption simultaneously. Based on this design, we can obtain the convergent rate $\mathcal{O}(\Delta t^2+h^2+H^{\frac{5}{2}})$ in three-dimension space, which means that the space mesh size satisfies $h=\mathcal{O}(H^\frac{5}{4})$. We also present two examples to verify our theorem.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2019-0371
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 2 : pp. 481–502
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Maxwell's equation two-grid algorithm Nédélec element postprocessing superconvergence.
Author Details
-
A reduced-order two-grid method based on POD technique for the semilinear parabolic equation
Song, Junpeng
Rui, Hongxing
Applied Numerical Mathematics, Vol. 205 (2024), Iss. P.240
https://doi.org/10.1016/j.apnum.2024.07.012 [Citations: 0]