1,720,986 research outputs found
Land subsidence due to gas/oil production in inhomogeneous transversally anisotropic half space by a boundary element method
No full textNumerical Approximation for Functionals of Reflecting Diffusion Processes
No full textThe aim of this paper is to approximate the expectation of a large class of functionals of the solution (X,xi) of a stochastic differential equation with normal reflection in a piecewise smooth domain of Rd . This also yields a Monte Carlo method for solving partial differential problems of parabolic type with mixed boundary conditions. The approximation is based on a modified Euler scheme for the stochastic differential equation. The scheme can be driven by a sequence of bounded independently and identically distributed (i.i.d.) random variables, or, when the domain is convex, by a sequence of Gaussian i.i.d. random variables. The order of (weak) convergence for both cases is given. In the former case the order of convergence is 1/2, and it is shown to be exact by an example. In the last section numerical tests are presented. The behavior of the error as a function of the final time T, for fixed values of the discretization step, and as a function of the discretization step, for fixed values of the final time T, is analyzed
Computing Expansion Coefficients in Orthogonal Bases of Ultraspherical Polynomials
No full textAbstractAlternative forms are proposed for the coefficients in the series expansions of certain orthogonal functions. An application is made to the expansion in series of ultraspherical polynomials. Advantages in the numerical calculation of such coefficients, similar to those previously obtained by P.J. Scanlon for the case of Legendre polynomials, are shown to continue to exist. Numerical examples are given to illustrate the attainable accuracy
Linear Galerkin vs mixed finite element 2D flow fields
No full textNumerical velocity fields arising from the solution of diffusion equations by the finite element (FE) and the mixed hybrid finite element (MHFE) schemes display different behaviors. In this paper we analyze the characteristics of the two different velocity fields in terms of both accuracy and mass balance properties. General theoretical findings are mostly concerned with the asymptotic behavior of the numerical schemes, i.e. they look at properties as the mesh size tends to zero. For practical applications, it is necessary to work with a fixed mesh of given size. Thus, we attempt to characterize the numerical flow field accuracy by analyzing the resulting mass balance characteristics on a fixed mesh. The comparison is carried out by using direct local mass balance evaluations and by calculating streamlines. We detail the important differences, advantages, and disadvantages of the two approaches. In particular, we show that both FE and MH are perfectly conservative (up to the residual of the linear system solution) if proper control volumes are used. MH streamlines are admissible, i.e. numerical normal fluxes across cell interfaces are continuous. Since continuity of the normal fluxes is not guaranteed by FE, the resulting streamlines are less accurate
A DMLPG refinement technique for 2D and 3D potential problems
Full text linkMeshless Local Petrov Galerkin (MLPG) methods are pure meshless techniques for solving Partial Differential Equations (PDE). MLPG techniques are nowadays used for solving a huge number of complex, real–life problems. While MLPG aims to approximate the solution of a given differential problem, its “dual” Direct MLPG (DMLPG) technique relies upon approximating linear functionals. Assume adaptive methods are to be implemented. When using a mesh–based method, inserting and/or deleting a node implies complex adjustment of connections. Meshless methods are more apt to implement adaptivity, since they does not require such adjustments. Nevertheless, ad–hoc insertion and/or deletion algorithms must be devised, in order to attain a good accuracy. In this paper we introduce a fresh refinement technique for DMLPG methods. Nodes are inserted in a discretization cloud where the local variation in the solution is supposed to be “large”. The variation is estimated using the (local) Total Variation (TV). DMLPG allows to directly estimate the partial derivatives, in order to compute the TV. MLPG must rely upon approximating the derivatives of the shape functions, hence MLPG refinement results to be more involved than its DMLPG counterpart. We show that our DMLPG refinement procedure allows one to efficiently solve a given diffusion problem whose solution undergoes large variations on a small portion of the domain. The accuracy afforded by a fine uniform cloud can be attained by using far less non–uniformly arranged nodes
Numerical solution for the one-phase Stefan problem by piecewise constant approximation of the interface
No full textThe classical one-phase one-dimensional Stefan problem is numerically solved on rectangles, Rj, of increasing size controlled by the Stefan condition. This approach is based on a scheme introduced by E. Di Benedetto and R. Spigler in 1983. The practical implementation rests on the representation via thermal potentials of the solution uj(x, t) to the heat equation in Rj. The quantity uxj(xj, jΔt) which determines the (j+1)-th rectangle is evaluated analytically by solving explicitly an integral equation. The solution in Rj+1 is then obtained by numerically evaluating a further integral expression. The algorithm is tested by solving two problems whose solution is explicitly known. Convergence, stability and convergence rate as Δx→0, Δt→0 have been tested and plots are shown. © 1990 Springer-Verlag
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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