Dissertation > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis

Research on h-, P-, hp-Adaptive Element Methods

Author BaiSiLin
Tutor YuChunXiao
School Yanshan University
Course Computational Mathematics
Keywords Adaptive Boundary Element Methods Sobolev spaces Posteriori error estimates Boundary integral equation h - layered adaptive boundary element method p- layered adaptive boundary element method hp- layered adaptive boundary element method
CLC O241
Type Master's thesis
Year 2009
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Are two important types of papers on adaptive boundary element method , h- and p- adaptive boundary element method to do a detailed study of layered superimposed on this basis , its shape function , h- and p - layered adaptive boundary element method and error analysis ; instance of h- and p- layered adaptive boundary element method compares the performance , combining the advantages of both algorithms to develop a new combination hp- layered adaptive boundary element method, and applied to the classical problem of elasticity , further development of the adaptive boundary element technology . The thesis is divided into five chapters, the first chapter is an introduction section , an overview of the boundary element method , adaptive research and development of the boundary element method , and pointed out that this issue is the source of the content and significance . Chapter II established the framework of the Sobolev space , research in this framework, adaptive method for realizing a posteriori error estimation theory , adaptive boundary element method , a posteriori error estimates expressions and specific adaptive process . The process of establishing the boundary integral equation , provides a theoretical basis for the latter chapters of the study . Chapter of the h- layered adaptive boundary element method specific studies, given the equation solving hierarchical algorithm , a the interpolation residual error estimation method for its adaptive characteristics . Chapter IV presents the p- layered adaptive boundary element method to do a detailed discussion on the choice of the shape function , highlight the iterative algorithm equation solving , according to its adaptive characteristics given two calculations simple error methods of analysis Chapter application instance Adaptive Boundary Element Methods for h- and p- layered performance through comparative analysis and in calculating the structural similarities , and work out a new set the hp- layered adaptive iterative scheme of the boundary element method , and gives specific examples to prove the effectiveness and superiority of this method .

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