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![]() ![]() The error analysis determines what methods will be combined. Similar to the Finite Element method, Moving least squares uses a linear algebraic system to solve for the approximate solution.įinally a hybrid method will first do an error analysis between each method. Meshfree methods for the solution of partial differential equations gained much attention in recent years, not only in the engineering but also in the. This method uses the geometry at a point instead of an element. On the other hand, the meshfree method (EFG) will use the same uniform mesh as the Finite Element Method as well as a scatter plot for direct comparisons using rectangular support domains. The elements are then used to form a matrix equation using the Galerkin form of the PDE and solve the system for the approximate solution. ![]() A one-to-four refinement method can then be applied to each triangle to produce a uniform mesh. Each of the triangles in the domain is called an element. The mesh method (Finite Element Method) uses a uniform partition of the domain called a triangulation. This process will be repeated for many domains and PDES problems of the form Lu=f. The program will produce the domain and the solution of the problem graphically as well as give relative error between the exact solution and the approximate solution. From this framework, a computational program will be implemented for mesh, meshfree and the hybrid method. The mesh and meshfree methods will be studied from a theoretical framework. The last part will provide a method for combining the mesh and meshless methods for a hybrid method. Meshfree methods for the solution of partial differential equations gained much attention in recent years, not only in the engineering but also in the mathematics community. The second part (Chapter two) will be developing the meshless method. Meshfree Methods for Partial Differential Equations III (Lecture Notes in Computational Science and Engineering, 57) 129.83 In Stock. The first part is chapter one which develops the finite element method. This manuscript will be divided into three main parts. The second purpose of this project is to determine if a hybrid between the mesh and meshless method is beneficial. Textbooks by Liu 3 and Fasshauer 4 discuss meshfree methods, implementation, algorithms, and coding issues for stress-strain problems Liu 3. The first purpose is to compare two types of Galerkin methods: The finite element mesh method and moving least sqaures meshless Galerkin (EFG) method. There are two purposes of this research project. ![]()
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