Rate of convergence

About: Rate of convergence is a research topic. Over the lifetime, 31257 publications have been published within this topic receiving 795334 citations. The topic is also known as: convergence rate.

An unfitted finite element method using discontinuous Galerkin

Abstract: In this paper we present a new approach to simulations on complex-shaped domains. The method is based on a discontinuous Galerkin (DG) method, using trial and test functions defined on a structured grid. Essential boundary conditions are imposed weakly via the DG formulation. This method offers a discretization where the number of unknowns is independent of the complexity of the domain. We will show numerical computations for an elliptic scalar model problem in ℝ 2 and ℝ 3 . Convergence rates for different polynomial degrees are studied.

Topological solutions in the self-dual chern-simons theory - existence and approximation

Abstract: In this paper a globally convergent computational scheme is established to approximate a topological multivortex solution in the recently discovered self-dual Chern-Simons theory in R 2 . Our method which is constructive and numerically efficient finds the most superconducting solution in the sense that its Higgs field has the largest possible magnitude. The method consists of two steps: first one obtains by a convergent monotone iterative algorithm a suitable solution of the bounded domain equations and then one takes the large domain limit and approximates the full piane solutions. It is shown that with a special choice of the initial guess function, the approximation sequence approaches exponentially fast a solution in R 2 . The convergence rate implies that the truncation errors away from local regions are insignificant.

2-D solution for free vibrations of parabolic shells using generalized differential quadrature method

Abstract: The Generalized Differential Quadrature (GDQ) procedure is developed for the free vibration analysis of complete parabolic shells of revolution and parabolic shell panels The First-order Shear Deformation Theory (FSDT) is used to analyze the above moderately thick structural elements The treatment is conducted within the theory of linear elasticity, when the material behaviour is assumed to be homogeneous and isotropic The governing equations of motion, written in terms of internal resultants, are expressed as functions of five kinematic parameters, by using the constitutive and kinematic relationships The solution is given in terms of generalized displacement components of the points lying on the middle surface of the shell The discretization of the system by means of the Differential Quadrature (DQ) technique leads to a standard linear eigenvalue problem, where two independent variables are involved The results are obtained taking the meridional and circumferential co-ordinates into account, without using the Fourier modal expansion methodology Several examples of parabolic shell elements are presented to illustrate the validity and the accuracy of GDQ method Numerical solutions are compared with the ones obtained using commercial programs such as Abaqus, Ansys, Femap/Nastran, Straus, Pro/Mechanica Very good agreement is observed Furthermore, the convergence rate of natural frequencies is shown to be very fast and the stability of the numerical methodology is very good The accuracy of the method is sensitive to the number of sampling points used, to their distribution and to the boundary conditions Different typologies of non-uniform grid point distributions are considered The effect of the distribution choice of sampling points on the accuracy of GDQ solution is investigated New numerical results are presented

Persistence of excitation conditions and the convergence of adaptive schemes

Abstract: In the study of the behavior of adaptive filtering algorithms, persistence of excitation of the input process arises as a sufficient condition for convergence and, perhaps more importantly, for convergence rate of the parameter estimates. In this paper the underlying nature of the persistence requirement is presented and discussed, relating its normal specification in terms of moment conditions with covariance decays, etc., to sample path properties. Deterministic and stochastic persistence conditions and persistence measures are treated, as well as, persistence conditions for output-error, equation-error, and adaptive control schemes.