Error Analysis Of Dimension Splitting Element Free Galerkin Method For Solving Three Dimensional Linear Partial Differential Equations

Dimension splitting element free Galerkin method(DSEFG)is an important numerical method in meshless methods.Firstly,the three-dimensional problem is divided into two dimensional problem and one-dimensional problem.The improved element free Galerkin method is used in the two-dimensional problem,and the finite difference method is used in one direction.This paper introduces the mathematical theory of element free Galerkin method.Based on the element free Galerkin method(EFG),this paper presents the derivation of DSEFG algorithm for three-dimensional potential problems and three-dimensional convection diffusion problems.For the three-dimensional potential problem,specific numerical example is given,the effects of splitting direction,node distribution,proportion parameter of influence domaind_max and penalty factor ? on relative error and running time of DSEFG method are studied.The relative error and running time of DSEFG method and IEFG method are compared and analyzed.The results of DSEFG method are compared with those of the improved element free Galerkin method(IEFG)in terms of relative error and running time.For the three-dimensional convection diffusion problem,the effects of panel point distribution,influence domain scale parameterd_max,penalty factor ?,dimension splitting level and time step?t on the relative error of DSEFG method is studied by specific numerical example.The corresponding error diagram is made with origin.The relative error between DSEFG method and IEFG method is compared and analyzed.For the general linear partial differential equation,the time of DSEFG method is shorter than that of IEFG method when the relative error is similar,and the number of nodes distribution is related to the domain of the problem itself.The larger the domain of definition,the more nodes are divided,and thed_max is generally between 1.0 and 2.0.