this approach is that we build both a minimizing measure and a solution of the generalized eikonal equation at the same time. Furthermore the approximations are smooth, and so we can derive some interesting formulas u...
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this approach is that we build both a minimizing measure and a solution of the generalized eikonal equation at the same time. Furthermore the approximations are smooth, and so we can derive some interesting formulas upon differentiating the Euler-Lagrange equation. Our method is inspired by the "calculus of variations in the sup-norm" ideas of Aronsson, Jensen, Barron and others.
A free boundary formulation for the numerical solution of boundaryvalueproblems on infinite intervals was proposed recently in Fazio (SIAM J. Nurner. Anal. 33 (1996) 1473). We consider here a survey on recent develo...
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A free boundary formulation for the numerical solution of boundaryvalueproblems on infinite intervals was proposed recently in Fazio (SIAM J. Nurner. Anal. 33 (1996) 1473). We consider here a survey on recent developments related to the free boundary identification of the truncated boundary. The goals of this survey are: to recall the reasoning for a free boundary identification of the truncated boundary, to report on a comparison of numerical results obtained for a classical test problem by three approaches available in the literature, and to propose some possible ways to extend the free boundary approach to the numerical solution of problems defined on the whole real line. (C) 2002 Elsevier Science B.V. All rights reserved.
The symmetric coupling of mixed finite element and boundary element methods is analysed for a model interface problem with the Laplacian. The coupling involves a further continuous ansatz function on the interface to ...
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The symmetric coupling of mixed finite element and boundary element methods is analysed for a model interface problem with the Laplacian. The coupling involves a further continuous ansatz function on the interface to link the discontinuous displacement field to the necessarily continuous boundary ansatz function. Quasi-optimal a priori error estimates and sharp a posteriori error estimates are established which justify adaptive mesh-refining algorithms. numerical experiments prove the adaptive coupling as an efficient tool for the numerical treatment of transmission problems.
The etalon boundary-value problem technique for approximately solving three-dimensional diffraction problems has been suggested. On etalon boundary-valueproblems, we use two-dimensional problems which are capable of ...
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The etalon boundary-value problem technique for approximately solving three-dimensional diffraction problems has been suggested. On etalon boundary-valueproblems, we use two-dimensional problems which are capable of exact solutions (for example, by the Wiener-Hopf technique). The field sought along one of the coordinate axes is taken to be locally coincident with that in the corresponding etalon problem. The amplitude coefficient (constant for the etalon problem) is assumed to be varying and is determined by substituting the above-mentioned solution representation into wave equations. Applications of the approach developed for the problem of electromagnetic-wave coastal refraction for a coast with a curved (random) coastal line and for the problem of wave diffraction by a perfectly conducting half-plane with a curvilinear edge have been considered.
We consider a Galerkin finite element method that uses piecewise bilinears on a modified Shishkin mesh for a model singularly perturbed convection-diffusion problem on the unit square. The method is shown to be conver...
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We consider a Galerkin finite element method that uses piecewise bilinears on a modified Shishkin mesh for a model singularly perturbed convection-diffusion problem on the unit square. The method is shown to be convergent, uniformly in the perturbation parameter epsilon, of order N-1 in a global energy norm, provided only that epsilon less than or equal to N-1, where O(N-2) mesh points are used. Thus on the new mesh the method yields more accurate results than on Shishkin's original piecewise uniform mesh, where it is convergent of order N-1 In N. numerical experiments support our theoretical results.
An explicit solution of elementary nature is derived for a mixed initial/boundaryvalue problem concerning the two-dimensional diffusion equation, given an arbitrarily assigned behaviour along a semi-infinite line and...
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An explicit solution of elementary nature is derived for a mixed initial/boundaryvalue problem concerning the two-dimensional diffusion equation, given an arbitrarily assigned behaviour along a semi-infinite line and a vanishing normal derivative along the remainder of the line;and the physically significant variation of the normal derivative at the boundary is similarly expressed.
The present work deals with the numerical solution of elliptic flows encountered in open-ended channels, The important question of applying boundary conditions for pressure and velocity for these flows is considered a...
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The present work deals with the numerical solution of elliptic flows encountered in open-ended channels, The important question of applying boundary conditions for pressure and velocity for these flows is considered and a new method for the application of boundary conditions at the channel inlet is proposed. It is shown that the flow reversal at the channel outlet, which appears when nonsymmetric flow conditions are present, is strongly dependent on the entrance boundary conditions for pressure. Results for the straight channel in situations where flow reversal is present are reported for a wide range of Rayleigh numbers. solutions for L-shaped channels are also reported with the aim of demonstrating the application of the model to arbitrary channels. II is shown that for certain flow situations the use of all elliptic formulation is imperative in order to predict correctly the flow behavior in open-ended channels.
Estimates for the Dirichlet eigenfunctions near the boundary of an open, bounded set in euclidean space are obtained. It is assumed that the boundary satisfies a uniform capacitary density condition.
Estimates for the Dirichlet eigenfunctions near the boundary of an open, bounded set in euclidean space are obtained. It is assumed that the boundary satisfies a uniform capacitary density condition.
The subject is the 2-point boundaryvalue problem for a second order ordinary differential equationformula herethe simplest and oldest of all boundaryvalueproblems, which arose in Euler's work on calculus of var...
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The subject is the 2-point boundaryvalue problem for a second order ordinary differential equationformula herethe simplest and oldest of all boundaryvalueproblems, which arose in Euler's work on calculus of variations in the eighteenth century. Accordingly, there is a vast literature, mostly in the context of applied mathematics, where one frequently uses the methods of functional *** we adopt a different point of view: we look for the number of solutions of problem (1), if any, and how this number varies with the endpoints (t1, x1) and (t2, x2). The concept of focal decomposition, introduced in [15] and developed by Peixoto and Thom in [19], expresses precisely this point of view (see §2). It was further developed by Kupka and Peixoto in [10] in the context of geodesics. From there, one is led naturally to relationships with the arithmetic of positive definite quadratic forms, a line that is considered in [16]. In both [10] and [16] attention is drawn to the close formal relationship between focal decomposition and the Brillouin zones of solid state physics. In [17] this line is pursued further and it is pointed out that the focal decomposition associated to (1) appears naturally as a prerequisite for the semiclassical quantization of this equation via the Feynman path integral *** main goal of the present paper is to prove Theorem 2, stated at the end of §4. There we give a functional +t2t1L (t, x, xÙ) dt and consider its Euler equation. To this second order differential equation we associate the corresponding focal decomposition. Theorem 2 gives a criterion on the Lagrangian L from which we get a rough geometric description of this focal decomposition. It turns out to be somewhat similar to the one associated to the pendulum equation x¨+sin x = 0, worked out by Peixoto and Thom in [19, pp. 631, 197]. In the case L = (xÙ2/2) V(x) this type of focal decomposition is generic in some topological sense. [ABSTRACT FROM AUTHOR]
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