Supraconvergence of elliptic finite difference schemes: general boundary condit...

• Author(s): Ferreira, J. A.
• Date: 2004
• Persistent ID: http://hdl.handle.net/10316/11411
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Nonuniform grids; Finite difference scheme; Stability; Supraconvergence; Superconvergence of gradient
• Document Type: Preprint
• Language: English

Description

In this paper we study the convergence properties of a finite difference discretization of a second order elliptic equation with mixed derivatives and variable coefficient in polygonal domains subject to general boundary conditions. We prove that the finite difference scheme on nonuniform grids exhibit the phenomenon of supraconvergence, more precisely, for s ∈ [1, 2] order O(hs)-convergence of the finite difference solution and its gradient if the exact solution is in the Sobolev space Hs+1(). Centro de Matemática da Universidade de Coimbra; Project POCTI/35039/MAT/2000