Analysis of Two-Grid Characteristic Finite Element Methods for Convection-Diffusion Equations. (18th January 2023)

• Record Type: Journal Article
• Authors: Wang, Keyan; Hu, Boxia
• Other Names: Gobithaasan R. U. Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2023(2023)
• Publication Date: 2023-01-18
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2023/6322303
• Languages: English
• ISSNs: 2314-4629

Abstract

Abstract : In this paper, two efficient two-grid algorithms for the convection-diffusion problem with a modified characteristic finite element method are studied. We present an optimal error estimate in L p -norm for the characteristic finite element method unconditionally, while all previous works require certain time-step restrictions. To linearize the characteristic method equations, two-grid algorithms based on the Newton iteration approach and the correction method are applied. The error estimate and the convergence result of the two-grid method are derived in detail. It is shown that the coarse space can be extremely coarse and achieve asymptotically optimal approximations as long as the mesh sizes H = O h 1 / 3 in the first algorithm and H = O h 1 / 4 in the second algorithm, respectively. Finally, two numerical examples are presented to demonstrate the theoretical analysis.