H-r, H-p Adaptive Boundary Element Methods And Error Estimates

Adaptive boundary element method is a powerful tool. The basic idea is to automatically determine and improve the accuracy of the boundary element solution using the computer. The mesh optimization and error estimates are very important. Especially a posteriori error estimates, it not only gives a precision estimate of the numerical results, but guide the algorithm. Obviously, it is very meaningful to study the adaptive processes and error estimates.When using adaptive boundary element, analysis need define discrete boundary grids to reflect the geometric features, and specify the boundary element solution's accuracy, the computer will automatically begin an iterative process to generate discrete grids. In this paper, different adaptive methods and error estimates schemes are proposed, and their effectiveness has been verified.Firstly, it systematically expounds the boundary element methods and the adaptive boundary element methods. Then, we study the theory of posteriori error estimates through which the adaptive methods is realized.Secondly, we put forward a new error estimation of H-R adaptive boundary element, and work out the program of H-R adaptive boundary element.Then, the H-P adaptive boundary element method is proposed. Meanwhile, we describe the data structure. In addition, we use the form of the norm as the error factor in the adaptive process. Later, we work out the program of the H-P adaptive boundary element to solve the problem about plane elastostatics.Finally, we analysis some special models of elastic problem with error estimate proposed and the adaptive method expounded. At the same time, we discuss the results and make sure that the adaptive boundary element method based on posteriori error estimates are completely feasible, which well validates the efficiency and superiority of them and their extensive application value in practical engineering.