| Summary: | 碩士 === 東海大學 === 數學系 === 99 === In recent years, meshfree methods have emerged into a new class of computational methods and have been widely applied to scientific and engineering problems. Meshfree methods can be roughly divided into two categories: one is based on weak formulation and the other is based on strong formulation. In this work, we provide a framework of coupling of reproducing kernel particle method (RKPM) and finite element method (FEM) for solving boundary value problems. This work focuses on the error analysis both under weak formulation and on the construction of discrete systems. The construction and mathematical analysis for RKPM are quite similar to FEM, but the accuracy of the solution by former is higher than that by latter. Furthermore, the dimension of discrete system of RKPM does not vary when the reproducing degree increased, the discrete system from RKPM costs more CPU time than FEM. The strategy of an optimal coupling, for example, the relationship between the meshsize of FEM and the nodal distant and reproducing degree of RKPM, is discussed in this work as well.
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