Résolution d’un problème aux limites dans un ouvert axisymétrique par éléments finis en $r, z$ et séries de Fourier en $\theta $

Mercier, Bertrand; Raugel, Geneviève

doi:10.1051/m2an/1982160404051

Cited by 108 publications

(117 citation statements)

References 4 publications

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“…In [11], the reason for the introduction of integral degrees of freedom was (incorrectly) given to be the lack of continuity of the functional v → v(0, z) in H 2 1 (D). However, this functional is indeed continuous in H 2 1 (D), as shown in [15,Theorem 4.7]. Relying on this continuity, an alternate approach to approximation theory in H 2 1 (D) is pursued in [15].…”

Section: Approximation On Rectangular Meshesmentioning

confidence: 98%

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A mixed method for axisymmetric div-curl systems

2008

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Abstract. We present a mixed method for a three-dimensional axisymmetric div-curl system reduced to a two-dimensional computational domain via cylindrical coordinates. We show that when the meridian axisymmetric Maxwell problem is approximated by a mixed method using the lowest order Nédélec elements (for the vector variable) and linear elements (for the Lagrange multiplier), one obtains optimal error estimates in certain weighted Sobolev norms. The main ingredient of the analysis is a sequence of projectors in the weighted norms satisfying some commutativity properties.

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Section: Approximation On Rectangular Meshesmentioning

confidence: 98%

“…Relying on this continuity, an alternate approach to approximation theory in H 2 1 (D) is pursued in [15]. However, [15] does not give the other projectors and the commutativity properties in (4.2) needed for the analysis of mixed methods. …”

Section: Approximation On Rectangular Meshesmentioning

confidence: 99%

A mixed method for axisymmetric div-curl systems

2008

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“…The reduction of three-dimensional problems to axisymmetric ones is addressed in the early work by Mercier and Raugel [42] (for Poisson problems) and by Belhachmi, Bernardi, and Deparis [3] and Belhachmi et al [4] for the Stokes and Navier-Stokes equations in the primitive variables and by Carneiro de Araujo and Ruas [17] for a three-field formulation.…”

Section: Related Workmentioning

confidence: 99%

A Stabilized Finite Volume Element Formulation for Sedimentation-Consolidation Processes

Bürger¹,

Ruiz–Baier²,

Torres³

2012

SIAM J. Sci. Comput.

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Abstract.A model of sedimentation-consolidation processes in so-called clarifier-thickener units is given by a parabolic equation describing the evolution of the local solids concentration coupled with a version of the Stokes system for an incompressible fluid describing the motion of the mixture. In cylindrical coordinates, and if an axially symmetric solution is assumed, the original problem reduces to two space dimensions. This poses the difficulty that the subspaces for the construction of a numerical scheme involve weighted Sobolev spaces. A novel finite volume element method is introduced for the spatial discretization, where the velocity field and the solids concentration are discretized on two different dual meshes. The method is based on a stabilized discontinuous Galerkin formulation for the concentration field, and a multiscale stabilized pair of P 1 -P 1 elements for velocity and pressure, respectively. Numerical experiments illustrate properties of the model and the satisfactory performance of the proposed method.

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“…Furthermore, if g denotes any of these functions, g, g r , g belong to L 2 r 2 . Then, according to [13], r 1 2 g(0) can be defined in a weak sense and the value is 0. Thus, introducing the new functions…”

Section: Variational Formulation In a Bounded Domainmentioning

confidence: 99%