Convergence of the Neumann series in BEM for the Neumann problem of the Stokes system
نویسندگان
چکیده
A weak solution of the Neumann problem for the Stokes system in Sobolev space is studied in a bounded Lipschitz domain with connected boundary. A solution is looked for in the form of a hydrodynamical single layer potential. It leads to an integral equation on the boundary of the domain. Necessary and sufficient conditions for the solvability are given. Moreover, it is shown that we can obtain a solution of this integral equation using the successive approximation method. Then the consequences for the direct boundary integral equation method are treated. A solution of the Neumann problem for the Stokes system is the sum of the hydrodynamical single layer potential corresponding to the boundary condition and the hydrodynamical double layer potential corresponding to the trace of the velocity part of the solution. The boundary behavior of potentials leads to an integral equation on the boundary of the domain where the trace of the velocity part of the solution is an unknown. It is shown that we can obtain a solution of this integral equation using the successive approximation method.
منابع مشابه
Saint-Venant torsion of non-homogeneous anisotropic bars
The BEM is applied to the solution of the torsion problem of non-homogeneous anisotropic non-circular prismatic bars. The problem is formulated in terms of the warping function. This formulation leads to a second order partial differential equation with variable coefficients, subjected to a generalized Neumann type boundary condition. The problem is solved using the Analog Equation Method (AEM)...
متن کاملDamage identification of structures using second-order approximation of Neumann series expansion
In this paper, a novel approach proposed for structural damage detection from limited number of sensors using extreme learning machine (ELM). As the number of sensors used to measure modal data is normally limited and usually are less than the number of DOFs in the finite element model, the model reduction approach should be used to match with incomplete measured mode shapes. The second-order a...
متن کاملA Boundary Meshless Method for Neumann Problem
Boundary integral equations (BIE) are reformulations of boundary value problems for partial differential equations. There is a plethora of research on numerical methods for all types of these equations such as solving by discretization which includes numerical integration. In this paper, the Neumann problem is reformulated to a BIE, and then moving least squares as a meshless method is describe...
متن کاملApproximate solution of fourth order differential equation in Neumann problem
Generalized solution on Neumann problem of the fourth order ordinary differential equation in space $W^2_alpha(0,b)$ has been discussed, we obtain the condition on B.V.P when the solution is in classical form. Formulation of Quintic Spline Function has been derived and the consistency relations are given.Numerical method,based on Quintic spline approximation has been developed. Spline solution ...
متن کاملAsymptotic distributions of Neumann problem for Sturm-Liouville equation
In this paper we apply the Homotopy perturbation method to derive the higher-order asymptotic distribution of the eigenvalues and eigenfunctions associated with the linear real second order equation of Sturm-liouville type on $[0,pi]$ with Neumann conditions $(y'(0)=y'(pi)=0)$ where $q$ is a real-valued Sign-indefinite number of $C^{1}[0,pi]$ and $lambda$ is a real parameter.
متن کامل