TY  - EJOU
AU  - Shirzadi, Ahmad 

TI  - Meshless Local Integral Equations Formulation for the 2D Convection-Diffusion Equations with a Nonlocal Boundary Condition
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2012
VL  - 85
IS  - 1
SN  - 1526-1506

AB  - This paper presents a meshless method based on the meshless local integral equation (LIE) method for solving the two-dimensional diffusion and diffusion-convection equations subject to a non-local condition. Suitable finite difference scheme is used to eliminate the time dependence of the problem. A weak formulation on local subdomains with employing the fundamental solution of the Laplace equation as test function transforms the resultant elliptic type equations into local integral equations. Then, the Moving Least Squares (MLS) approximation is employed for discretizing spatial variables. Two illustrative examples with exact solutions being used as benchmark solutions are presented to show the efficiency of the proposed method.
KW  - Meshless methods
KW  -  Local integral equations
KW  -  Nonlocal integral condition
KW  -  Time dependent problems
KW  -  Finite differences

DO  - 10.3970/cmes.2012.085.045