| Summary: | 碩士 === 國立宜蘭大學 === 土木工程學系碩士班 === 98 === In order to overcome the drawback of obtaining reliable error estimation the numerical methods in solving realistic engineering problems when an analytical solution is not available, we developed a systematic error estimation scheme in this thesis to estimate the numerical error in the numerical methods without having an analytical solution. In this thesis, a new problem is defined to substitute for the original problem. The governing equation, domain shape and boundary condition type in the new problem are the same as those in the original problem. By adopting the complete Trefftz set as the analytical solution, the analytical solution in the new problem is the known, namely quasi-analytical solution, which is similar with the real analytical solution in the original problem. After implementing numerical methods in the new problem, the error curves can be derived by comparing with the quasi-analytical solution in the new problem. By observing the error curve, we obtained the optimal number of elements or the optimal parameter in the numerical methods at the corner region in the error curve. Therefore, we developed a systematic error estimation scheme in this thesis to estimate the numerical error in the numerical methods. In this thesis, we apply the error estimation technique the boundary element method and the method of fundamental solutions to solve the Laplace problem and several numerical examples are taken to demonstrate the accuracy and efficiency of the proposed estimation technique
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