Moving Meshes Method Based On Natural Boundary Reduction For Exterior Elliptic Equation Problems

Based on the principle of natural boundary reduction,moving meshes method of elliptical boundary value problems in unbounded region is studied,and the contents are mainly divided into three chapters:In chapter 1,the research progress and application of natural boundary element method and non-uniform meshes method are introduced,respectively.The related mathematical theories are also mentioned.In chapter 2,we use NBEM and the coupling of NBEM and FEM to study the moving meshes method of harmonic equation in exterior concave region,boundary reduction principle is applied to obtain the natural integral equation on the circular arc boundary and the natural integral equation on the circular arc artificial boundary.Meanwhile,natural boundary element method and the coupling of NBEM-FEM method are constructed.We also analysis the constringency of the variational problem and convergence of the approximate solution.In the end,numerical example is presented to show the feasibility and effectiveness of the method.In chapter 3,NBEM and the coupling of NBEM and FEM are applied to study the moving meshes method of quasilinear equation in unbounded region,by the boundary reduction principle,we obtain the circular boundary condition and the circular artificial boundary condition,respectively.According to it,natural boundary element method and the coupling of NBEM-FEM method are constructed.The constringency of the variational problem and convergence of the approximate solution are analysised.In the end,numerical example is presented to show the feasibility and effectiveness of this method.