Two-grid scheme of expanded mixed finite element method for semilinear parabolic integro-differential equations

• Published in: Applicable analysis Vol. 101; no. 8; pp. 3017 - 3038
• Main Authors: Hou, Tianliang, Jiang, Wenzhu, Chen, Luoping
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 24.05.2022; Taylor & Francis Ltd
• Subjects: a priori error estimate; C. Bacuta; Crank-Nicolson scheme; Differential equations; Finite element analysis; Finite element method; Mathematical analysis; mixed finite element method; Semilinear parabolic integro-differential equations; Taylor series; two-grid
• ISSN: 0003-6811; 1563-504X
• DOI: 10.1080/00036811.2020.1834087

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.