Nonlinear elliptic problems with the method of finite volumes. (19th October 2006)

• Record Type: Journal Article
• Authors: Khattri Khattri, Sanjay Kumar Sanjay Kumar
• Is Part Of: Differential equations and nonlinear mechanics. Volume 2006/2006)
• Publication Date: 2006-10-19
• Subjects: Differential equations, Nonlinear -- Periodicals; Nonlinear mechanics -- Periodicals; Équations différentielles non linéaires; Mécanique non linéaire; Differential equations, Nonlinear; Nonlinear mechanics; Chaos Theory; Differential Equations; Periodicals; Electronic journals; 515.35
• DOI: 10.1155/DENM/2006/31797
• Languages: English
• ISSNs: 1687-4099

Abstract

Abstract : We present a finite volume discretization of the nonlinear elliptic problems. The discretization results in a nonlinear algebraic system of equations. A Newton-Krylov algorithm is also presented for solving the system of nonlinear algebraic equations. Numerically solving nonlinear partial differential equations consists of discretizing the nonlinear partial differential equation and then solving the formed nonlinear system of equations. We demonstrate the convergence of the discretization scheme and also the convergence of the Newton solver through a variety of practical numerical examples.