Analytical and numerical solutions of a class of nonlinear integro-differential equations with L1 kernels. (February 2020)

• Record Type: Journal Article
• Authors: Xu, Da
• Is Part Of: Nonlinear analysis. Volume 51(2020)
• Publication Date: 2020-02
• Subjects: Nonlinear and nonlocal hyperbolic integro-differential equations -- L1 weakly singular kernel -- Global existence and uniqueness -- Galerkin methods -- Euler methods -- Optimal error estimates; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.103002
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We study the finite element approximations to a general class of nonlinear and nonlocal hyperbolic integro-differential equations with L 1 convolution kernels. The continuous time Galerkin procedures are defined and global existence of a unique discrete solution is derived. Moreover, optimal error estimates are shown in the L ∞ ( H 0 1 ( Ω ) ) -norms. For the completely discrete scheme, linearized backward Euler method is defined and error estimates in l ∞ ( H 0 1 ( Ω ) ) -norm are proved. Several numerical experiments are reported to confirm our theoretical findings.