Boundary Integral Equation With The Galerkin Method And The Least Squares Method For Elliptic Boundary Value Problem To Deal With

There are many papers(cf[l]-[3])have studied the method and error estimate for boundary integeral equation and elliptic boundary value problems , and obtain some superconvergent results by varied post-processings such as interpolation , average and extrapolation etc.In this paper, we mainly study the Galerkin solution for first-kind boundary Integeral equation and elliptic boundary value preblem. Further more we can obtain superconvergence results by (L₂ project ion) Least-squares processing for derivative of elliptic boundary value problems.In part one, we dissuss the Galerkin method and error estimate for first-kind boundary integeral equation derived by forrowing exterior Dirichlet problemsThen result in superconvergent results by Least-squares processing.Next, in part two, we discuss the Galerkin method forelliptic value problemsand obtain superconvergent results of derivative by Least-square processing. Farther more, we prove that we can also obtain superconvergecnt results by Least-squares processing for derivative directly.Finally, by examples we verified that Least-squares processing really result in better results.