Catálogo de publicaciones - libros

For the linear finite element approximation to a linear elliptic model problem, we propose to safeguard the Zienkiewicz-Zhu estimator by an additional estimator for the residual of the averaged gradient. We give a brief account of the theoretical results on reliability, (local) efficiency, and asymptotic exactness of the full estimator and illustrate these properties in numerical tests, incorporating singular solutions and anisotropic ellipticity.

We analyse some questions concerning splitting solution techniques of non-hydrostatic models with atmospheric forcing. We prove that at the free surface the dynamic pressure must exactly vanish. We also analyse a linearised model of free surface and give simple rules to construct stable pairs of (horizontal velocities, free surfaces) for mixed discretizations.

The goal of this paper is to construct efficient finite volume parallel solvers on non-structured grids for 2d hyperbolic systems of conservation laws with source terms and nonconservative products using SIMD registers. Line method is applied: at every intercell a projected Riemann problem along the normal direction is considered (see [2]). The resulting 2d numerical schemes are explicit and first order accurate. The solver is parallelized following a SIMD approach, by means of SSE (“”), which are present in common processors. A generic C++ wrapper to small matrices libraries that make use of SIMD instructions has been implemented in an efficient way and an application to IPP small matrix library is presented.

An optimal control problem for a 2-d elliptic equation and with pointwise control constraints is investigated. The domain is assumed to be polygonal but non-convex. The corner singularities are treated by a priori mesh grading. A second order approximation of the optimal control is constructed by a projection of the discrete adjoint state. Here we summarize the results from [1] and add further numerical tests.

A posteriori analysis has become an inherent part of numerical mathematics. Methods of a posteriori error estimation for finite element approximations were actively developed in the last two decades (see, e.g., [1, 2, 3, 12] and the references therein). For problems in the theory of optimization, these methods started receiving attention much later. In particular, for optimal control problems governed by PDEs the literature on this matter is rather scarce. In this work, we present a new approach to a class of optimal control problems associated with elliptic type partial differential equations. In the framework of this approach, we obtain directly computable upper bounds for the cost functionals of the respective optimal control problems.

Mathematical modelling of air lubrication phenomena taking place during read/write processes in magnetic storage devices (hard-disks, for example) can be addressed by using a compressible Reynolds equation for the air pressure. In the present paper, we propose a duality algorithm with optimal functional parameters to numerically solve the nonlinear diffusive term. A theoretical result is stated and some numerical examples are presented to illustrate the performance of the method.

We present some stabilized methods for a nonstationary advectiondiffusion problem. The methods are designed by combining of some stabilized finite element methods and Discontinuous Galerkin time integration. Numerical experiments are presented comparing the new schemes with the space time elements of [3].

This paper is devoted to the numerical solution of two-dimensional steady scalar convection-diffusion equations using the finite element method. If the popular streamline upwind/Petrov-Galerkin (SUPG) method is used, spurious oscillations usually arise in the discrete solution along interior and boundary layers. We review various finite element discretizations designed to diminish these oscillations and we compare them computationally.

An algebraic approach to the design of high-resolution finite element schemes for convection-dominated flows is pursued. It is explained how to get rid of nonphysical oscillations and remove excessive artificial diffusion in regions where the solution is sufficiently smooth. To this end, the discrete transport operator and the consistent mass matrix are modified so as to enforce the positivity constraint in a mass-conserving fashion. The concept of a and a new definition of upper/lower bounds make it possible to design a general-purpose flux limiter which provides an optimal treatment of both stationary and time-dependent problems.

In this paper we consider the local Modified Extrapolated Gauss-Seidel() method combined with Semi-Iterative techniques for the numerical solution of the Convection Diffusion equation and compare it with the local method. AMS(MOS), 65F10. Parallel Iterative methods, linear systems, semi-iterative methods, Fourier analysis, Gauss-Seidel method, convection diffusion equation.