1,721,313 research outputs found
FOURIER SPECTRAL METHODS FOR PSEUDO-PARABOLIC EQUATIONS
No full textFourier spectral methods of Galerkin and collocation type for quasilinear pseudo-parabolic equations are presented. Convergence with spectral accuracy is proved for both Galerkin and collocation approximations. Unconditionally stable discretization in time by explicit one-step methods is analyzed. Fast transform methods to compute the nonlinear terms are proposed
MIXED APPROXIMATIONS OF EVOLUTION PROBLEMS
No full textAn analysis of a finite element method for a system of partial differential equations having a noncoercive stationary part is developed. Applications to the vibrations of an elastic plate and to Schrodinger's equation are discussed. For the semidiscrete problem and for two implicit difference schemes convergence results in the L**2-norm and in the energy norm are proved. Finally some results related to model problems are shown
Mathematical models for the technology and the science of life[Modelli matematici per la tecnologia e le scienze della vita]
No full textIn this presentation I will review some mathematical models that are used to describe complex phenomena in real life. Applications will concern aeronautics, hydrodynamics, medicine, environmental flow problems, and problems arising from sport competition. For environmental studies, mathematical models are used to predict, analyze and, possibly, control events of relevant social impact. In sport, mathematical models are often used to try to enhance performances of athlets as well as to improve the design of vehicles that are used in the various disciplines. In medicine, we will explain how mathematics can be used in the study of the cardiovascular system in order to better understand physiological blood flow processes and design alternative therapeutical surgery. More in general, we will highlight the role of scientific computing in everyday analysis of problems of real life interest
ON MIXED METHODS FOR FOURTH-ORDER PROBLEMS
No full textA mixed finite element method for the problem upsilon plus sigma **2 DELTA **2 upsilon equals chi with different types of boundary conditions is described. The method converges, and it is well suited for the analysis of various evolution problems. The computation of the discrete solution is made by applying a sequence of iterative methods for block matrices: correspondingly to each iteration either a couple of Poisson problems or a couple of problems for the identity operator are solved, according to the value of the parameter sigma . Some numerical results for two model examples are presented
Modellistica Numerica per Problemi Differenziali
No full textIn questo testo si introducono i concetti elementari di modellistica numerica di problemi differenziali alle derivate parziali. Si considerano le classiche equazioni lineari ellittiche, paraboliche ed iperboliche, ma anche altre equazioni, quali quelle di diffusione e trasporto, di Navier-Stokes, e le leggi di conservazione, e si forniscono numerosi esempi fisici che stanno alla base di tali equazioni. Quindi si analizzano metodi di risoluzione numerica basati su elementi finiti, differenze finite e metodi spettrali. Il volume è adatto agli studenti dei corsi di laurea di indirizzo scientifico (Ingegneria, Fisica, Matematica, Chimica, Scienza dell'Informazione) e consigliato ai ricercatori del mondo accademico ed extra-accademico che vogliano avvicinarsi a questo interessante ramo della matematica applicata
Domain decomposition techniques using spectral methods
No full textThe main domain decomposition techniques currently in use in connection with approximation by spectral methods are reviewed. Their most relevant features concerning both the theoretical and the computational aspects are analyzed. Some applications to the Helmholtz problem, to the convection-diffusion equation and to the transport equation are shown.
© 1987 Instituto di Elaborazione della Informazione del CNR
Hybrid finite element methods for the von Karman equations
No full textWe analyse the «assumed stresses» hybrid approximation of the Von Karman equations; we provide convergence results and optimal error bounds for a large class of finite element discretizations.
© 1980 Instituto di Elaborazione della Informazione del CNR
Some results of bernstein and jackson type for polynomial approximation in Lp-spaces
No full textThis work is motivated by the analysis of stability and convergence of spectral methods using Chebyshev and Legendre polynomials. We investigate the properties of the polynomial approximation to a function u in the norms of the weighted Lwp (-1, 1) spaces. p is any real number between 1 and ∞, and w(x) is either the Chebyshev or the Legendre weight. The estimates are given in terms of the degree N of the polynomials and of the smoothness of u. They include and generalize some theorems of Jackson. Some Bernstein-type inequalities are also given. © 1984 JJAM Publishing Committee
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