Abstract
Many meshless methods have been proposed to release the formidable task of mesh generation of traditional FEM. However, there yet exit some problems on the way of improving the practicability of meshless methods. Among them, the linear independence of approximation functions should be guaranteed easily, otherwise the nodes have to be distributed with extreme attention to linear independence and the freedom of meshless methods will be limited very much. In this paper, a new meshless approximation method, Cover Least Square Approximation, is proposed. The approximation is constructed on the Finite Cover System by approaching the cover functions as closely as possible. Some properties of Cover Least Square Approximation, such as continuity, interpolatory, reproducibility and linear independence, are discussed. Since the linear independence conditions can be simply satisfied, it can be practicably implemented.
