A Hessian recovery-based finite difference method for biharmonic problems. (March 2023)

• Record Type: Journal Article
• Authors: Xu, Minqiang; Shi, Chungang
• Is Part Of: Applied mathematics letters. Volume 137(2023)
• Publication Date: 2023-03
• Subjects: Hessian recovery technique -- Ghost points method -- Superconvergence -- Biharmonic problems; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2022.108503
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this paper, we study a new finite difference method by combining Hessian recovery techniques and the ghost points method for biharmonic equations. Numerical results validate that our proposed method has optimal convergence orders in the L 2 norm and H 1 seminorm. Moreover, superconvergence properties of the recovered gradient and Hessian have been observed.