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Displaying 221 –
240 of
499
In this article, we provide a priori error estimates for the spectral and
pseudospectral Fourier (also called planewave) discretizations of the
periodic Thomas-Fermi-von Weizsäcker (TFW) model and for the spectral
discretization of the periodic Kohn-Sham
model, within the local density approximation (LDA). These models
allow to compute approximations of the electronic ground state energy and density
of molecular systems in the condensed phase. The TFW model is strictly
convex with respect to the...
In this work, the quasistatic thermoviscoelastic thermistor problem is
considered. The thermistor model describes the combination of the effects due to
the heat, electrical current conduction and Joule's heat generation. The variational
formulation leads to a coupled system of nonlinear variational equations for which
the existence of a weak solution is recalled.
Then, a fully discrete algorithm is introduced based on the finite element
method to approximate the spatial variable and an Euler scheme...
In this paper, we present a numerical approach to evolution of decohesion
in laminated composites based on incremental variational problems. An energy-based framework is adopted, in which we characterize the system by the stored energy and dissipation functionals quantifying reversible and irreversible processes, respectively. The time-discrete evolution then follows from a solution of incremental minimization problems, which are converted to a fully discrete form by employing the conforming finite...
A conceptual numerical strategy for rate-independent processes in the
energetic formulation is proposed and its convergence is proved under various
rather mild data qualifications. The novelty is that we obtain convergence of
subsequences of space-time discretizations even in case where the limit
problem does not have a unique solution and we need no
additional assumptions on higher regularity of the limit solution.
The variety of general perspectives thus
obtained is illustrated on several...
Computational analysis of quasi-brittle fracture in cement-based and similar composites, supplied by various types of rod, fibre, etc. reinforcement, is crucial for the prediction of their load bearing ability and durability, but rather difficult because of the risk of initiation of zones of microscopic defects, followed by formation and propagation of a large number of macroscopic cracks. A reasonable and complete deterministic description of relevant physical processes is rarely available. Thus,...
2000 Mathematics Subject Classification: 26A33 (primary), 35S15In this paper, a space fractional diffusion equation (SFDE) with nonhomogeneous
boundary conditions on a bounded domain is considered. A
new matrix transfer technique (MTT) for solving the SFDE is proposed.
The method is based on a matrix representation of the fractional-in-space
operator and the novelty of this approach is that a standard discretisation
of the operator leads to a system of linear ODEs with the matrix raised
to the...
2000 Mathematics Subject Classification: 26A33 (primary), 35S15 (secondary)This paper provides a new method and corresponding numerical schemes
to approximate a fractional-in-space diffusion equation on a bounded domain
under boundary conditions of the Dirichlet, Neumann or Robin type.
The method is based on a matrix representation of the fractional-in-space
operator and the novelty of this approach is that a standard discretisation
of the operator leads to a system of linear ODEs with the matrix...
We study a numerical method for the diffusion of an age-structured population in a spatial environment. We extend the method proposed in [2] for linear diffusion problem, to the nonlinear case, where the diffusion coefficients depend on the total population. We integrate separately the age and time variables by finite differences and we discretize the space variable by finite elements. We provide stability and convergence results and we illustrate our approach with some numerical result.
In this paper we consider a hyperbolic-parabolic problem that models the longitudinal deformations of a thermoviscoelastic rod supported unilaterally by an elastic obstacle. The existence and uniqueness of a strong solution is shown. A finite element approximation is proposed and its convergence is proved. Numerical experiments are reported.
In this paper we consider a hyperbolic-parabolic problem that models the longitudinal deformations of a thermoviscoelastic rod supported unilaterally by an elastic obstacle. The existence and uniqueness of a strong solution is shown. A finite element approximation is proposed and its convergence is proved. Numerical experiments are reported.
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499