A frame theory encompassing general relativity and Newton–Cartan theory is reviewed. With its help, a definition is given for a one-parameter family of general relativistic spacetimes to have a Newton–Cartan or a Newtonian limit. Several examples of such limits are presented. PACS numbers: 0420, 0240, 0450

We analyze the XMM-Newton dataset of the interacting cluster of galaxies Abell 3528 located westward in the core of the Shapley Supercluster, the largest concentration of mass in the nearby Universe. A3528 is formed by two interacting clumps (A3528-N at North and A3528-S at South) separated by 0.9 h −1 70 Mpc at redshift 0.053. XMM-Newton data describe these clumps as relaxed structure with an ...

In this paper, we investigate the convergence behaviour of a class of regularized Newton methods for the solution of nonlinear inverse problems. In order to keep the overall numerical effort as small as possible, we propose to solve the linearized equations by certain semiiterative regularization methods, in particular, iterations with optimal speed of convergence. Our convergence rate analysis...

In recent years a number of authors have considered an error analysis for quadrature rules of Newton-Cotes type. In particular, the mid-point, trapezoid and Simpson rules have been investigated more recently ([2], [4], [5], [6], [11]) with the view of obtaining bounds on the quadrature rule in terms of a variety of norms involving, at most, the first derivative. In the mentioned papers explicit...

We present techniques for implicit solution of discontinuous Galerkin discretizations of the Navier-Stokes equations on parallel computers. While a block-Jacobi method is simple and straight-forward to parallelize, its convergence properties are poor except for simple problems. Therefore, we consider Newton-GMRES methods preconditioned with block-incomplete LU factorizations, with optimized ele...

We study optimal stochastic (or Monte Carlo) quadrature formulas for convex functions. While nonadaptive Monte Carlo methods are not better than deterministic methods we prove that adaptive Monte Carlo methods are much better. Abstract. We study optimal stochastic (or Monte Carlo) quadrature formulas for convex functions. While nonadaptive Monte Carlo methods are not better than deter-ministic ...

In some applications of Galerkin boundary element methods one has to compute integrals which, after proper normalization, are of the form ∫ b a ∫ 1 −1 f(x, y) x− y dxdy, where (a, b) ≡ (−1, 1), or (a, b) ≡ (a,−1), or (a, b) ≡ (1, b), and f(x, y) is a smooth function. In this paper we derive error estimates for a numerical approach recently proposed to evaluate the above integral when a p−, or h...

We reformulate the discretization of the Johnson–Nedelec method [11] of coupling boundary elements and finite elements for an exterior bidimensional Laplacian. This new formulation leads to optimal error estimates and allows the use of simple quadrature formulas for calculation of the boundary element matrix. We show that if the parameter of discretization is sufficiently small, the fully discr...