Karaa, S. (2007) High-Order Difference Scheme for 2D Elliptic and Parabolic Problems with Mixed Derivatives. Numerical Methods for Partial Differential Equations, 23, 366-378.
http://dx.doi.org/10.1002/num.20181

has been cited by the following article:

• TITLE: High Order Compact Difference Scheme and Multigrid Method for 2D Elliptic Problems with Variable Coefficients and Interior/Boundary Layers on Nonuniform Grids

  AUTHORS: Bin Lan, Yongbin Ge, Yan Wang, Yong Zhan

  KEYWORDS: Elliptic Equation, Coordinate Transformation, High Order Compact Difference Scheme, Multigrid Method, Interior/Boundary Layer

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.3 No.5, May 19, 2015

  ABSTRACT: In this paper, a high order compact difference scheme and a multigrid method are proposed for solving two-dimensional (2D) elliptic problems with variable coefficients and interior/boundary layers on nonuniform grids. Firstly, the original equation is transformed from the physical domain (with a nonuniform mesh) to the computational domain (with a uniform mesh) by using a coordinate transformation. Then, a fourth order compact difference scheme is proposed to solve the transformed elliptic equation on uniform girds. After that, a multigrid method is employed to solve the linear algebraic system arising from the difference equation. At last, the numerical experiments on some elliptic problems with interior/boundary layers are conducted to show high accuracy and high efficiency of the present method.