A full discretization for the saddle-point approach of a degenerate parabolic problem involving a moving body. (February 2022)

• Record Type: Journal Article
• Authors: Le, Van Chien; Slodička, Marián; Van Bockstal, Karel
• Is Part Of: Applied mathematics letters. Volume 124(2022)
• Publication Date: 2022-02
• Subjects: Degenerate parabolic problem -- Moving body -- Saddle-point formulation -- Finite element method; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2021.107660
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: This paper aims to study a degenerate parabolic problem for a solenoidal vector field in which the time derivative acts on a moving body. We propose a fully-discrete finite element scheme combined with backward Euler's method for the saddle-point variational formulation. The convergence of this numerical scheme is proved and error estimates for some stable finite element pairs are also established.