Content:Development and research situation of the meshless method are given,we mainly research the meshless local Petrov-Galerkin (MLPG) applying to the unstable well flow of groundwater,the calculation format of the unstable well flow of groundwater is introduced. In this paper,there are five sections.In the first section,we introduce the research background about the meshless local Petrov-Galerkin (MLPG) method and the research work of this paper.In the second section,we give out the recent main results of radial basis functions and weighted residual method.In the third section,we describe the basic theory of the meshless local Petrov-Galerkin(MLPG) method to which the flow problem of groundwater solved.In the fourth section, we use the meshless local Petrov-Galerkin(MLPG) method based on radial basis function to discuss the unstable well flow of groundwater, and an example is given,the rationality of the method discussed in this paper is proved by this example.In the fifth section,we make a summary of the paper and give an outlook of the future research direction.
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