%0 Journal Article
%T High Order Compact Difference Scheme and Multigrid Method for 2D Elliptic Problems with Variable Coefficients and Interior/Boundary Layers on Nonuniform Grids
%A Bin Lan
%A Yongbin Ge
%A Yan Wang
%A Yong Zhan
%J Journal of Applied Mathematics and Physics
%P 509-523
%@ 2327-4379
%D 2015
%I Scientific Research Publishing
%R 10.4236/jamp.2015.35063
%X 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.
%K Elliptic Equation
%K Coordinate Transformation
%K High Order Compact Difference Scheme
%K Multigrid Method
%K Interior/Boundary Layer
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=56416