Superconvergence analysis of a linearized three‐step backward differential formula finite element method for nonlinear Sobolev equation. (21st March 2019)

• Record Type: Journal Article
• Authors: Wang, Junjun; Li, Qingfu
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 9(2019)
• Page Start: 3359
• Page End: 3376
• Publication Date: 2019-03-21
• Subjects: bilinear element -- linearized BDF‐3 Galerkin FEM -- nonlinear Sobolev equation -- superconvergence results -- temporal error and spatial error; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5589
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : A linearized three‐step backward differential formula (BDF) Galerkin finite element method (FEM) is developed for nonlinear Sobolev equation with bilinear element. Temporal error and spatial error are discussed through introducing a time‐discrete system. Solutions of the time‐discrete system are bounded in H 2 ‐norm by the temporal error. Superconvergence results of order O ( h 2 + τ 3 ) in H 1 ‐norm for the original variable are deduced based on the spatial error. Some new tricks are utilized to get higher order of the temporal error and the spatial error. At last, two numerical examples are provided to support the theoretical analysis. Here, h is the subdivision parameter, and τ is the time step.