Two grid finite element discretization method for semi‐linear hyperbolic integro‐differential equations. Issue 5 (7th March 2019)

• Record Type: Journal Article
• Authors: Chen, Luoping; Chen, Yanping; Huang, Yunqing
• Is Part Of: Numerical methods for partial differential equations. Volume 35:Issue 5(2019)
• Page Start: 1676
• Page End: 1693
• Publication Date: 2019-03-07
• Subjects: error estimate -- finite element method -- semi‐linear hyperbolic integro‐differential equations -- two‐grid discretization; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22370
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : In this paper, we will investigate a two grid finite element discretization method for the semi‐linear hyperbolic integro‐differential equations by piecewise continuous finite element method. In order to deal with the semi‐linearity of the model, we use the two grid technique and derive that once the coarse and fine mesh sizes H, h satisfy the relation h = H 2 for the two‐step two grid discretization method, the two grid method achieves the same convergence accuracy as the ordinary finite element method. Both theoretical analysis and numerical experiments are given to verify the results.