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Displaying 721 –
740 of
1688
The paper deals with some mixed finite element methods on a class of anisotropic meshes based on tetrahedra and prismatic (pentahedral) elements. Anisotropic local interpolation error estimates are derived in some anisotropic weighted Sobolev spaces. As particular applications, the numerical approximation by mixed methods of the Laplace equation in domains with edges is investigated where anisotropic finite element meshes are appropriate. Optimal error estimates are obtained using some anisotropic...
The paper deals with some mixed finite element methods on a class
of anisotropic meshes based on tetrahedra and prismatic (pentahedral)
elements. Anisotropic local
interpolation error estimates are derived in some anisotropic weighted Sobolev
spaces. As particular
applications, the numerical approximation by mixed methods of the Laplace equation
in domains
with edges is investigated where anisotropic finite
element meshes are appropriate. Optimal error estimates are obtained using
some anisotropic...
We derive in this article some models of
Cahn-Hilliard equations in nonisotropic media. These models, based on
constitutive equations introduced by Gurtin in [19], take the work of
internal microforces and also the deformations of the material into
account. We then study the existence and uniqueness of solutions and
obtain the existence of finite dimensional attractors.
We give examples of parabolic systems (in space dimension ) having a solution with real analytic initial and boundary values which develops the discontinuity in the interior of the parabolic cylinder.
We consider a family of conforming finite element schemes with piecewise polynomial space of degree in space for solving the wave equation, as a model for second order hyperbolic equations. The discretization in time is performed using the Newmark method. A new a priori estimate is proved. Thanks to this new a priori estimate, it is proved that the convergence order of the error is in the discrete norms of and , where and are the mesh size of the spatial and temporal discretization, respectively....
Some new oscillation criteria are obtained for second order elliptic differential equations with damping
, x ∈ Ω,
where Ω is an exterior domain in ℝⁿ. These criteria are different from most known ones in the sense that they are based on the information only on a sequence of subdomains of Ω ⊂ ℝⁿ, rather than on the whole exterior domain Ω. Our results are more natural in view of the Sturm Separation Theorem.
We present some new problems in spectral optimization. The first one consists in determining the best domain for the Dirichlet energy (or for the first eigenvalue) of the metric Laplacian, and we consider in particular Riemannian or Finsler manifolds, Carnot-Carathéodory spaces, Gaussian spaces. The second one deals with the optimal shape of a graph when the minimization cost is of spectral type. The third one is the optimization problem for a Schrödinger potential in suitable classes.
We study the nonstationary Navier-Stokes equations in the entire three-dimensional space and give some criteria on certain components of gradient of the velocity which ensure its global-in-time smoothness.
In order to accommodate solutions with multiple
phases, corresponding to crossing rays, we
formulate geometrical optics for the scalar wave equation as
a kinetic transport equation set in phase space.
If the maximum number of phases is finite and known a priori we
can recover the exact multiphase solution from an
associated system of moment equations, closed by an assumption
on the form of the density function in the kinetic equation.
We consider two different closure assumptions based on
delta...
Currently displaying 721 –
740 of
1688