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The Partition of Unity Method on the Basis of Local Polynomial Approximation Spaces and Its Error Analysis

Author: SuFang
Tutor: HuangYunQing
School: Xiangtan University
Course: Computational Mathematics
Keywords: Meshless Method Unit decomposition method Local approximation space Maximum modulus estimates L2 Norm Estimates
CLC: O241.82
Type: Master's thesis
Year: 2005
Downloads: 94
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Abstract


In recent years , meshless methods are applied to the scientific and engineering computing , a common feature of such methods is no longer need the grid structure when dealing with large deformation , moving boundary problems and other difficult issues , they are very effective. The unit decomposition method is a mesh - free methods , the feature of this method is that it contains not only the knowledge of the finite element solution of partial differential equations , it is more efficient than the finite element method . This paper is divided into three parts . The first part , we present the basic mathematical theory of the partition of unity method , depending on the problem , the local approximation space selection is different . Here , we detail analysis unit decomposition method based on local polynomial approximation space , and pointed out that the local approximation space of basis functions multiplied not necessarily after the partition of unity function the unit decomposition space base , they may be linearly related to the subsequent given the types of interpolation polynomial local approximation space . Second part we first error of the finite element method convergence order start decomposition method for a special class of units (whichever is the usual finite element basis function units decomposition) analysis , and prove that the order of error than the partition of unity in the local space approximation order of an order . We have obtained the result of any number of partial spaces are established L 2 , the norm L ∞ , Norm also established . The third part , the author summarizes the general conclusion of this work , and combined with the existing work , and error analysis of the prospect .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations > Numerical Solution of Partial Differential Equations
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