A generalized finite difference method for solving biharmonic interface problems. (February 2022)

• Record Type: Journal Article
• Authors: Xing, Yanan; Song, Lina; Li, Po-Wei
• Is Part Of: Engineering analysis with boundary elements. Volume 135(2022)
• Page Start: 132
• Page End: 144
• Publication Date: 2022-02
• Subjects: Meshless method -- Generalized finite difference method -- Interface problems -- Biharmonic equation; 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.2021.11.001
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract : In this paper, a meshless discrete scheme based on the generalized finite difference method (GFDM) is proposed to solve the biharmonic interface problem. This scheme turns the interface problem to be two non-interface subproblems coupled with the interface conditions. The interface conditions act as the boundary conditions of the subproblems because the interface plays the role of their boundary. Therefore, the proposed method has the advantage of dealing with problems with complex geometrical interfaces. Due to the GFDM approximates the derivatives of the unknown variables by using a linear combination of the values for nearby nodes, the proposed method also has the advantage in dealing with the interface condition with the jump of derivatives. Four numerical examples are provided to verify the accuracy and the stability of the GFDM for biharmonic interface problems. The numerical results show that the H 1 errors can reach almost the same convergence rate of the L ∞ and L 2 errors. The convergence rates are almost and even higher than fourth-order when the fourth-order Taylor Series expansion is adopted in the GFDM.