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A higher order pressure segregation scheme for the time-dependent incompressible magnetohydrodynamics (MHD) equations is presented. This scheme allows us to decouple the MHD system into two sub-problems at each time step. First, a coupled linear elliptic system is solved for the velocity and the magnetic field. And then, a Poisson-Neumann problem is treated for the pressure. The stability is analyzed and the error analysis is accomplished by interpreting this segregated scheme as a higher order...
We address in this article the computation of the convex solutions of the Dirichlet problem for the real elliptic Monge − Ampère equation for general convex domains in two dimensions. The method we discuss combines a least-squares formulation with a relaxation method. This approach leads to a sequence of Poisson − Dirichlet problems and another sequence of low dimensional algebraic eigenvalue problems of a new type. Mixed finite element approximations with a smoothing procedure are used for the...
An extension of the local projection stabilization (LPS) finite element method for convection-diffusion-reaction equations is presented and analyzed, both in the steady-state and the transient setting. In addition to the standard LPS method, a nonlinear crosswind diffusion term is introduced that accounts for the reduction of spurious oscillations. The existence of a solution can be proved and, depending on the choice of the stabilization parameter, also its uniqueness. Error estimates are derived...
In this paper we propose and analyze a localized orthogonal decomposition (LOD) method for solving semi-linear elliptic problems with heterogeneous and highly variable coefficient functions. This Galerkin-type method is based on a generalized finite element basis that spans a low dimensional multiscale space. The basis is assembled by performing localized linear fine-scale computations on small patches that have a diameter of order H | log (H) | where H is the coarse mesh size. Without any assumptions...
The aim of this paper is to develop a finite element method which allows computing
the buckling coefficients and modes of a non-homogeneous Timoshenko beam.
Studying the spectral properties of a non-compact operator,
we show that the relevant buckling coefficients correspond to isolated
eigenvalues of finite multiplicity.
Optimal order error estimates are proved for the eigenfunctions
as well as a double order of convergence for
the eigenvalues using classical abstract spectral approximation theory...
The aim of this paper is to develop a finite element method which allows computing
the buckling coefficients and modes of a non-homogeneous Timoshenko beam.
Studying the spectral properties of a non-compact operator,
we show that the relevant buckling coefficients correspond to isolated
eigenvalues of finite multiplicity.
Optimal order error estimates are proved for the eigenfunctions
as well as a double order of convergence for
the eigenvalues using classical abstract spectral approximation theory...
In this paper we certify that the same approach proposed in previous works by Chniti et al. [C. R. Acad. Sci. 342 (2006) 883–886; CALCOLO 45 (2008) 111–147; J. Sci. Comput. 38 (2009) 207–228] can be applied to more general operators with strong heterogeneity in the coefficients. We consider here the case of reaction-diffusion problems with piecewise constant coefficients. The problem reduces to determining the coefficients of some transmission conditions to obtain fast convergence of domain decomposition...
In this paper we certify that the same approach proposed in previous works by Chniti et al. [C. R. Acad. Sci.342 (2006) 883–886; CALCOLO45 (2008) 111–147; J. Sci. Comput.38 (2009) 207–228] can be applied to more general operators with strong heterogeneity in the coefficients. We consider here the case of reaction-diffusion problems with piecewise constant coefficients. The problem reduces to determining the coefficients of some transmission conditions
to obtain fast convergence of domain decomposition...
We present in this article two components: these components can in fact serve various goals independently, though we consider them here as an ensemble. The first component is a technique for the rapid and reliable evaluation prediction of linear functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential features are (i) (provably) rapidly convergent global reduced–basis approximations — Galerkin projection onto a space spanned...
We present in this article two components: these components can in fact serve various goals
independently, though we consider them here as an ensemble. The first component is a technique for
the rapid and reliable evaluation prediction of linear functional outputs of elliptic (and
parabolic) partial differential equations with affine parameter dependence.
The essential features are (i) (provably) rapidly convergent global
reduced–basis approximations — Galerkin projection onto a space
WN spanned...
A Mimetic Discretization method for the linear elasticity problem
in mixed weakly symmetric form is developed. The scheme is shown to
converge linearly in the mesh size, independently of the
incompressibility parameter λ, provided the discrete scalar
product satisfies two given conditions. Finally, a family of
algebraic scalar products which respect the above conditions is
detailed.
A unilateral problem of an elastic plate above a rigid interior obstacle is solved on the basis of a mixed variational inequality formulation. Using the saddle point theory and the Herrmann-Johnson scheme for a simultaneous computation of deflections and moments, an iterative procedure is proposed, each step of which consists in a linear plate problem. The existence, uniqueness and some convergence analysis is presented.
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