The Mrm-Bem Analysis Of A Kind Of Elliptic Partial Differential Equation Boundary Value Problem

Elliptic partial differential equation boundary value problem is mainly used in solid mechanics and fluid dynamics, its numerical method focus on finite element, boundary element, difference method and so on. These methods are effective. However, in its analysis of the error, we found the main error was the boundary integral equation. When solving the boundary variational inequality and elliptic equation boundary value problem, the use of boundary element method-multiple reciprocity method has more advantages and applicabilities than the classical boundary element method, because it through the use of high-order solution and repeat the basic replacement, change the integral term of the region into the integral equation,which is convergence to a infinite series, and then combine with boundary element method, we can avoid dispersing the region in numerical calculation.This paper includes five chapters. The chapter 1 mainly introduces the development of BEM, variational inequality and solving elliptic partial differential equation boundary value problem by MRM-BEM.In chapter 2, we establish the Sobolev space based on the elliptic partial differential equation boundary value problem. Then introduce a complete set of theories in this space, such as: generalized solution, generalized function, generalized derivative, the trace theorem and Brezzi theory, equivalent norm theorem and so on.In chapter 3, we introduce some typical elliptic partial differential boundary value problem in the framework of the variation, and show its basic nature through specific examples.In chapter 4, we introduce the static friction problem of the elastomer contact, which obeies the law of Coulomb, establish its corresponding mathematical model, and gain the MRM integral equation of the homogeneous and nonhomogeneous Helmholtz value problem by MRM-BEM. Regularization for the nondifferentiable item of this kind of variational inequality. Change the problem into a similar MRM boundary variational inequality. Then the convergence analysis of the approximate solution and accurate solution for the MRM-BEM is presented. Finally, make the problem into a normal convexity extreme problem.In chapter 5, we use boundary element method and multiple reciprocity method to receive MRM boundary integral equation and MRM boundary variation equation of the buckling eigenvalue problem, and then obtain the expression of the error estimate between approximate solution and accurate solution. The numerical example shows that this method has faster convergence and higher precision.