Abstract. Bounds are obtained for the derivatives of the solution of a turning point problem. These results suggest a modification of the El-Mistikawy Werle finite difference scheme at the turning point. A uniform error estimate is obtained for the resulting method, and illustrative numerical results are given.
Abstract.In this paper, a Signorini problem is reduced to a variational inequality on the boundary, and a direct boundary element method is presented for its solution. Furthermore, error estimates for the approximate solutions of Signorini problems are given. In addition, we show that the Signorini problem may be formulated as a saddle-point problem on the boundary.
Abstract. The numerical solution of the Cauchy problem for elliptic equations is considered. We reformulate the original problem as a variational inequality problem, which we solve using the finite element method. Moreover, we prove the convergence of the approximate solution.Let <$> be a bounded open set in the space R" and d6^ be the boundary of fy. Then ßr = ty X (0, T) is a bounded open set in Rn+I. We discuss the following boundary value problem for the elliptic equation:Here A,,, X are functions of x and, moreover, = g(x). If there are no added restrictions to the solutions of (I), J. Hadamard [1] has pointed out that the solution of (I) is not continuously dependent on the Cauchy data. So problem (I) is an improperly posed problem. As the famous example of J. Hadamard has shown, it is impossible to solve this improperly posed problem by the classical theory of partial differential equations. But these types of problems arise naturally in many kinds of practical problems and therefore have required the attention of many mathematicians. First, M. M. Lavrentiev [2] has discussed bounded solutions of the Laplace equation in a special two-dimensional domain. These solutions are dependent on the Cauchy data continuously. After this L. E. Payne [3], [4] studied solutions of more general second-order elliptic equations, which are dependent on the Cauchy data continuously. Of course, it is necessary to add some restrictions to the domains and the solutions. In 1975 L. E. Payne outlined this problem in [5].
Abstract. The exterior boundary value problems of linear elastic equations are considered. A sequence of approximations to the exact boundary conditions at an artificial boundary is given. Then the original problem is reduced to a boundary value problem on a bounded domain. Furthermore, a finite element approximation of this problem and optimal error estimates are obtained.Finally, a numerical example shows the effectiveness of this method.
This work proposes a novel enriched finite element method (E-FEM) for structural dynamics analysis. We developed the enriched 3-node triangular and 4-node tetrahedral displacement-based elements (T-elements). The standard linear shape functions of these T-elements were enriched using interpolation cover functions over each patch of elements. We also introduced and compared different orders of cover functions; higher-order functions obtained higher computational performance. Subsequently, the forced and free vibration analyses were performed on various typical numerical examples. The proposed enriched finite element method generated more precise numerical results and ensured faster convergence than the original linear elements.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.