Arbitrary Placement of Secondary Nodes, and Error Control, in the Meshless Local Prtrov-Galerkin (MLPG) Method

초록

The truly meshless local Petrov-Galerkin method holds a great promise in solving boundary value problems, using a local symmetric weak form as a natural approach. In the present paper, in the context of MLPG and the meshless interpolation of a moving least squares type, a method which used primary and secondary nodes in the domain and on the global boundary is introduced in order to improve the accuracy of solution. The secondary nodes can be placed at any location where on needs to obtain a better resolution. The sub-domains for the shape functions in the MLS approximation aredefined only from the primary nodes, and the secondary nodes use the same sub-domains. The present mehtod is very useful in an adaptive calculation, because the secondary nodes can be easily added and/or moved without an additional mesh.