Two-grid scheme of expanded mixed finite element method for semilinear parabolic integro-differential equations. Issue 8 (24th May 2022)

• Record Type: Journal Article
• Authors: Hou, Tianliang; Jiang, Wenzhu; Chen, Luoping
• Is Part Of: Applicable analysis. Volume 101:Issue 8(2022)
• Page Start: 3017
• Page End: 3038
• Publication Date: 2022-05-24
• Subjects: C. Bacuta; Semilinear parabolic integro-differential equations -- mixed finite element method -- a priori error estimate -- two-grid -- Crank–Nicolson scheme; 49J20 -- 65N30; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1834087
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we present a two-grid scheme of expanded mixed finite element method combined with two second-order time discretization schemes for semilinear parabolic integro-differential equations and give a detailed convergence analysis. On the coarse grid space, we first use the Crank–Nicolson scheme to solve the original nonlinear problem at the first time step, then we utilize the Leap-Frog scheme at the rest time levels. Next, we make use of the known coarse mesh solution and Taylor expansion to infer the solution on the fine mesh space. Thus, we only need to solve the nonlinear problem once on the coarse grid space of the two-grid scheme. Finally, a numerical example is presented to verify the effectiveness of the proposed two-grid scheme.