Many science and engineering problems can be mathematically modeled as a boundary value problem. Thus, it is very important to build a method to solve for a boundary value problem. For some simple boundary value problems, for example, a two-dimensional Laplace equation, it may be possible to solve it analytically by separation of variables. However, in most applications, boundary value problems...

Most requirements elicitation methods do not explicitly provide a systematic way for deciding the boundary of the usage context that should be taken into account because it is essentially difficult to decide which context element should be included as the system requirements. If a developer explores the context boundary in an ad-hoc manner, the developer will be faced with the frame problem bec...

This paper investigates inexact Uzawa methods for nonlinear saddle point problems. We prove that the inexact Uzawa method converges globally and superlinearly even if the derivative of the nonlinear mapping does not exist. We show that the Newton-type decomposition method for saddle point problems is a special case of a Newton-Uzawa method. We discuss applications of inexact Uzawa methods to se...

This paper proposes a novel meshless boundary method called the singular boundary method (SBM). This method is mathematically simple, easy-to-program, and truly meshless. Like the method of fundamental solutions (MFS), the SBM employs the singular fundamental solution of the governing equation of interest as the interpolation basis function. However, unlike the MFS, the source and collocation p...

We present a finite element method for the numerical solution of elliptic boundary value problems on stochastic domains. The method computes, to leading order in the amplitude of the stochastic boundary perturbation relative to an unperturbed, nominal domain, the mean and the variance of the random solution. The variance is computed as the trace of the solution’s two-point correlation which sat...

A symmetric-Galerkin boundary element framework for fracture analysis with frictional contact (crack friction) on the crack surfaces is presented. The algorithm employs a continuous interpolation on the crack surface (utilizing quadratic boundary elements) and enables the determination of two important quantities for the problem, namely the local normal tractions and sliding displacements on th...

In this paper we show that the h-p spectral element method developed in [3,8,9] applies to elliptic problems in curvilinear polygons with mixed Neumann and Dirichlet boundary conditions provided that the Babuska–Brezzi inf–sup conditions are satisfied. We establish basic stability estimates for a non-conforming h-p spectral element method which allows for simultaneous mesh refinement and variab...

In this paper, we consider the div-curl problem posed on nonconvex polyhedral domains. We propose a least-squares method based on discontinuous elements with normal and tangential continuity across interior faces, as well as boundary conditions, weakly enforced through a properly designed least-squares functional. Discontinuous elements make it possible to take advantage of regularity of given ...

6 The scaled boundary finite-element method (SBFEM) is a novel semi-analytical method 7 developed in the elasto-statics and elasto-dynamics areas that has the advantages of com8 bining the finite-element method with the boundary-element method. The SBFEM method 9 weakens the governing differential equation in the circumferential direction and solves the 10 weakened equation analytically in the ...