14,184 research outputs found
A Two-Level Method for Mimetic Finite Difference Discretizations of Elliptic Problems
We propose and analyze a two-level method for mimetic finite difference
approximations of second order elliptic boundary value problems. We prove that
the two-level algorithm is uniformly convergent, i.e., the number of iterations
needed to achieve convergence is uniformly bounded independently of the
characteristic size of the underling partition. We also show that the resulting
scheme provides a uniform preconditioner with respect to the number of degrees
of freedom. Numerical results that validate the theory are also presented
The double of the doubles of Klein surfaces
A Klein surface is a surface with a dianalytic structure. A double of a Klein
surface is a Klein surface such that there is a degree two morphism (of
Klein surfaces) . There are many doubles of a given Klein
surface and among them the so-called natural doubles which are: the complex
double, the Schottky double and the orienting double. We prove that if is a
non-orientable Klein surface with non-empty boundary, the three natural
doubles, although distinct Klein surfaces, share a common double: "the double
of doubles" denoted by . We describe how to use the double of doubles in
the study of both moduli spaces and automorphisms of Klein surfaces.
Furthermore, we show that the morphism from to is not given by the
action of an isometry group on classical surfaces.Comment: 14 pages; more details in the proof of theorem
Real closed exponential fields
In an extended abstract Ressayre considered real closed exponential fields
and integer parts that respect the exponential function. He outlined a proof
that every real closed exponential field has an exponential integer part. In
the present paper, we give a detailed account of Ressayre's construction, which
becomes canonical once we fix the real closed exponential field, a residue
field section, and a well ordering of the field. The procedure is constructible
over these objects; each step looks effective, but may require many steps. We
produce an example of an exponential field with a residue field and a
well ordering such that is low and and are ,
and Ressayre's construction cannot be completed in .Comment: 24 page
On the Virtual Element Method for Topology Optimization on polygonal meshes: a numerical study
It is well known that the solution of topology optimization problems may be
affected both by the geometric properties of the computational mesh, which can
steer the minimization process towards local (and non-physical) minima, and by
the accuracy of the method employed to discretize the underlying differential
problem, which may not be able to correctly capture the physics of the problem.
In light of the above remarks, in this paper we consider polygonal meshes and
employ the virtual element method (VEM) to solve two classes of paradigmatic
topology optimization problems, one governed by nearly-incompressible and
compressible linear elasticity and the other by Stokes equations. Several
numerical results show the virtues of our polygonal VEM based approach with
respect to more standard methods
Discontinuous Galerkin approximation of linear parabolic problems with dynamic boundary conditions
In this paper we propose and analyze a Discontinuous Galerkin method for a
linear parabolic problem with dynamic boundary conditions. We present the
formulation and prove stability and optimal a priori error estimates for the
fully discrete scheme. More precisely, using polynomials of degree on
meshes with granularity along with a backward Euler time-stepping scheme
with time-step , we prove that the fully-discrete solution is bounded
by the data and it converges, in a suitable (mesh-dependent) energy norm, to
the exact solution with optimal order . The sharpness of the
theoretical estimates are verified through several numerical experiments
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