A novel Green element method based on two sets of nodes. (June 2018)

• Record Type: Journal Article
• Authors: Rao, Xiang; Cheng, Linsong; Cao, Renyi; Jiang, Jun; Fang, Sidong; Jia, Pin; Wang, Lizhun
• Is Part Of: Engineering analysis with boundary elements. Volume 91(2018)
• Page Start: 124
• Page End: 131
• Publication Date: 2018-06
• Subjects: Green element method -- Two sets of nodes -- Second-order accuracy; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2018.03.017
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: This paper presented a novel Green element method (GEM) based on two sets of nodes, one of which contains all vertices of the polygon representing the value of the pressure, called pressure nodes, the other contains all midpoints of the edges of the polygon representing the value of the normal flux, called flux nodes. The novel method considers both the pressure and the normal flux explicitly, and utilizes the physical fact that, the algebraic sum of normal fluxes at the flux nodes which are on the edge shared by adjacent elements is zero. Therefore, the normal flux term at each internal flux node can be offset in the final global equations, and the order of the global coefficient matrix is only the number of pressure nodes. Compared to previous GEMs, the novel method has actual second-order accuracy. Moreover, because we selected the flux node at the midpoints of edges, the novel method made the solution process more in accordance with physical meaning, and the numerical solution has a better continuity in the computational domain than previous GEMs. It is worth mentioning that, to the authors' knowledge, this is the first time to utilize two sets of nodes when estimating the numerical solution to the problem described by only one differential equation. Therefore, the novel method may bring new ideas to other numerical methods, such as finite difference or finite element method, etc.