The Data Quality Monitoring (DQM) Software proved to be a central tool in the CMS experiment. Its flexibility allowed its integration in several environments: Online, for real-time detector monitoring; Offline, for the final, fine-grained Data Certification; ReleaseValidation, to constantly validate the functionality and the performance of the reconstruction software; in Monte Carlo productions...

A quadrature-based mixed Petrov-Galerkin finite element method is applied to a fourth-order linear ordinary differential equation. After employing a splitting technique, a cubic spline trial space and a piecewise linear test space are considered in the method. The integrals are then replaced by the Gauss quadrature rule in the formulation itself. Optimal order a priori error estimates are obtai...

where y(x) denotes the solution of the differential equation. The idea is to use a quadrature formula to estimate the integral of (1). This requires knowledge of the integrand at specified arguments x¿ in (xo, -To + h)—hence we require the values of y(x) at these arguments. A numerical integration method may be used to estimate y(x) for the required arguments. In this way a numerical integratio...