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Displaying 1081 –
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A number of approaches for discretizing partial differential equations with random data
are based on generalized polynomial chaos expansions of random variables. These constitute
generalizations of the polynomial chaos expansions introduced by Norbert Wiener to
expansions in polynomials orthogonal with respect to non-Gaussian probability measures. We
present conditions on such measures which imply mean-square convergence of generalized
polynomial...
The present work is a mathematical analysis of two algorithms, namely
the Roothaan and the level-shifting algorithms, commonly used in
practice to solve the Hartree-Fock equations. The level-shifting
algorithm is proved to be well-posed and to converge provided the shift
parameter is large enough. On the contrary, cases when the Roothaan
algorithm is not well defined or fails in converging are
exhibited. These mathematical results are confronted to numerical
experiments performed by chemists.
Si discretizza il problema dell'ostacolo parabolico con differenze all'indietro nel tempo ed elementi finiti lineari nello spazio e si dimostrano stime dell'errore per la frontiera libera discreta.
The backward Euler algorithm for the multidimensional nonhomogeneous heat equation is analyzed, based on the finite element method. The existence and uniqueness of the numerical solution is investigated. Also, the convergence of the numerical solutions is studied.
In this article we consider elliptic partial differential equations with random coefficients and/or random forcing terms. In the current treatment of such problems by stochastic Galerkin methods it is standard to assume that the random diffusion coefficient is bounded by positive deterministic constants or modeled as lognormal random field. In contrast, we make the significantly weaker assumption that the non-negative random coefficients can be bounded strictly away from zero and infinity by random...
In this paper we study the null-controllability of an artificial advection-diffusion system in dimension n. Using a spectral method, we prove that the control cost goes to zero exponentially when the viscosity vanishes and the control time is large enough. On the other hand, we prove that the control cost tends to infinity exponentially when the viscosity vanishes and the control time is small enough.
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