| Summary: | 碩士 === 國立成功大學 === 土木工程學系 === 102 === In this paper, we use the moving least square methods based on state variables and Hermite type collocation to solve the two-dimensional Poisson's equations, including the steady-state heat transfer and potential flow problems. The core concepts of the two numerical methods discussed in this paper are similar to the idea of Moving Least Squares Methods. Considering about governing equations, boundary conditions, and the minimal weighted sum of the approximation of state variables, the values of the approximate functions can be obtained. As a result, the accuracy of the numerical results is great.
In the numerical examples, we solved Poisson's equations with various boundary conditions, and we compared the numerical results with exact solutions to examine the accuracy and the rate of convergence of the two methods. In this paper we also discuss the influence on numerical accuracy due to different boundary conditions.
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