Variational Approximation in Modular Spaces by Using Finite Element Method Approach. (2nd January 2023)

• Record Type: Journal Article
• Authors: Mabdaoui, Mohamed; Moussa, Hicham; Rhoudaf, Mohamed
• Is Part Of: Numerical functional analysis and optimization. Volume 44:Number 1(2023)
• Page Start: 64
• Page End: 85
• Publication Date: 2023-01-02
• Subjects: Finite element method -- interpolation operators -- nonlinear elliptic problem -- Orlicz spaces; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2153367
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we shall study the polynomial approximation in a more general setting namely to consider the Orlicz-Sobolev spaces W k L M ( Ω ) . We study the local and global interpolation estimate and we will show the finite element error estimate for a nonlinear elliptic problem where we establish a generalization of Cea's Theorem and we prove the modular convergence of the gradient, then we present the existence result and its proof.