A Galerkin boundary node method and its convergence analysis

摘要

The boundary node method (BNM) exploits the dimensionality of the boundaryintegral equation (BIE) and the meshless attribute of the moving least-square (MIS)approximations. However, since MIS shape functions lack the property of a delta function,it is difficult to exactly satisfy boundary conditions in BNM. Besides, the system matricesof BNM are non-symmetric. A Galerkin boundary node method (GBNM) is proposed in this paper for solvingboundary value problems. In this approach, an equivalent variational form of a BIE is usedfor representing the governing equation, and the trial and test functions of the variationalformulation are generated by the MIS approximation. As a result, boundary conditionscan be implemented accurately and the system matrices are symmetric. Total detailsof numerical implementation and error analysis are given for a general BIE. Taking theDirichlet problem of Laplace equation as an example, we set up a framework for errorestimates of GBNM. Some numerical examples are also given to demonstrate the efficacityof the method.