Let I[f ] = ∫ 1 −1 f(x) dx, where f ∈ C ∞(−1, 1), and let Gn[f ] = ∑n i=1 wnif(xni) be the n-point Gauss–Legendre quadrature approximation to I[f ]. In this paper, we derive an asymptotic expansion as n → ∞ for the error En[f ] = I[f ]−Gn[f ] when f(x) has general algebraic-logarithmic singularities at one or both endpoints. We assume that f(x) has asymptotic expansions of the forms f(x) ∼ ∞ ∑ ...

We introduce a new family of symplectic integrators for canonical Hamiltonian systems. Each method in the family depends on a real parameter α. When α = 0 we obtain the classical Gauss collocation formula of order 2s, where s denotes the number of the internal stages. For any given non-null α, the corresponding method remains symplectic and has order 2s−2; hence it may be interpreted as an O(h2...

The family of PDE-constrained Large Deformation Diffeomorphic Metric Mapping (LDDMM) methods is emerging as a particularly interesting approach for physically meaningful diffeomorphic transformations. original combination Gauss–Newton–Krylov optimization and Runge–Kutta integration shows excellent numerical accuracy fast convergence rate. However, its most significant limitation the huge comput...

We study integration in a class of Hilbert spaces of analytic functions defined on the Rs. The functions are characterized by the property that their Hermite coefficients decay exponentially fast. We use Gauss-Hermite integration rules and show that the errors of our algorithms decay exponentially fast. Furthermore, we study tractability in terms of s and log ε−1 and give necessary and sufficie...

If the nodes for the spectral element method are chosen to be the Gauss-LegendreLobatto points, then the resulting mass matrix is diagonal and the method is sometimes then described as the Gauss-point mass lumped finite element scheme. We study the dispersive behaviour of the scheme issue in detail and provide both a qualitative description of the nature of the dispersive and dissipative behavi...

A multiscale formulation is derived for the mechanics of a dilute fiber network microstructure, as occurs in in vitro reconstituted collagen gels, to accommodate the deterministic solution of a uniform-stress condition in the fiber network. The macroscale two-phase equations are derived based on the integral volume-averaging approach of the spatial averaging theorem, modified for the averaging ...

We study singularities of Gauss maps (wave) fronts and give characterizations by geometric properties which are related to behavior bounded principal curvatures. Moreover, we investigate the relation between

Three discontinuous Galerkin methods (SIPG, NIPG, DG) are considered for solving a one-dimensional elliptic problem. Superconvergence for the error at the interior node points and the derivative of the error at Gauss points are considered. All theorectical results obtained in the paper are supported by the results of numerical experiments.

We compute point sets on the triangle that have low Lebesgue constant, with sixfold symmetries and Gauss-Legendre-Lobatto distribution on the sides, up to interpolation degree 18. Such points have the best Lebesgue constants among the families of symmetric points used so far in the framework of triangular spectral elements.

In the present study, the mechanical behavior of AA5052 aluminum alloy during cold deformation and subsequent isothermal annealing in a temperature range of 225-300oC was investigated using the uniaxial tensile test data. It is found that by increasing the annealing time and temperature the material yield strength is decreased. The microstructural investigations of the annealed samples show tha...