1,721,303 research outputs found
A Stabilization-Free Virtual Element Method for the Convection–Diffusion Eigenproblem
No full textThe aim of this paper is to propose and analyze a stabilization-free virtual element method for the non-selfadjoint convection-diffusion eigenvalue problem. The method is based on high order harmonic polynomial projections which are used to approximate the continuous sesquilinear forms. In order to analyze the continuous and discrete eigenvalue problems, we introduce solution operators and we prove convergence in norm. Then, by using the approximation spectral theory for compact non-selfadjoint operators, we show that the scheme provides a correct approximation of the spectrum and prove optimal error estimates for the eigenfunctions and a double order for the eigenvalues. The theoretical analysis considers only the case of quadrilateral meshes. Our study is supported by a series of numerical experiments, that assess the robustness of the method
Lowest order stabilization free Virtual Element Method for the 2D Poisson equation
Full text linkWe introduce and analyse the first order Enlarged Enhancement Virtual Element
Method (EVEM) for the Poisson problem. The method allows the definition of
bilinear forms that do not require a stabilization term, thanks to the
exploitation of higher order polynomial projections that are made computable by
suitably enlarging the enhancement (from which comes the prefix of the name
E) property of local virtual spaces. The polynomial degree of local
projections is chosen based on the number of vertices of each polygon. We
provide a proof of well-posedness and optimal order a priori error estimates.
Numerical tests on convex and non-convex polygonal meshes confirm the criterium
for well-posedness and the theoretical convergence rates.Comment: 35 pages, 8 figure
Emerging roles of DNA repair factors in the stability of centromeres
No full textSatellite DNA sequences are an integral part of centromeres, regions critical for faithful segregation of chro-mosomes during cell division. Because of their complex repetitive structure, satellite DNA may act as a barrier to DNA replication and other DNA based transactions ultimately resulting in chromosome breakage. Over the past two decades, several DNA repair proteins have been shown to bind and function at centromeres. While the importance of these repair factors is highlighted by various structural and numerical chromosome aberrations resulting from their inactivation, their roles in helping to maintain genome stability by solving the intrinsic difficulties of satellite DNA replication or promoting their repair are just starting to emerge. In this review, we summarize the current knowledge on the role of DNA repair and DNA damage response proteins in maintaining the structure and function of centromeres in different contexts. We also report the recent connection between the roles of specific DNA repair factors at these genomic loci with age-related increase of chromosomal instability under physiological and pathological conditions
SUPG-stabilized stabilization-free VEM: a numerical investigation
Full text linkWe numerically investigate the possibility of defining Stabilization-Free Virtual Element discretizations - i.e., Virtual Element Method discretizations without an additional non-polynomial non-operator-preserving stabilization term - of advection-diffusion problems in the advection-dominated regime, considering a Streamline Upwind Petrov-Galerkin stabilized formulation of the scheme. We present numerical tests that assess the robustness of the proposed scheme and compare it with a standard Virtual Element Method
A stabilization-free Virtual Element Method based on divergence-free projections
Full text linkIn this paper, we propose and analyze a Stabilization Free Virtual Element Method (SFVEM), that allows the definition of bilinear forms that do not require an arbitrary stabilization term, thanks to the exploitation of higher-order polynomial projections on divergence free vectors of polynomials. The method is introduced in the lowest order formulation for the Poisson problem. We provide a sufficient condition on the polynomial projection space that implies the well-posedness, proved on particular classes of polygons, and optimal order a priori error estimates. Numerical tests on convex and non-convex polygonal meshes confirm the theoretical convergence rates and show that the method is suitable for solving problems characterized by anisotropies
Stabilization-free Virtual Element Method for 2D second order elliptic equations
Full text linkIn this work, we present and analyze a Stabilization-free Virtual Element high order scheme for 2D second order elliptic equation. This method is characterized by the definition of new polynomial projections that allow the definition of structure-preserving schemes. We provide a necessary and sufficient condition on the polynomial projection space that ensure the well-posedness of the scheme and we derive optimal a priori error estimates. Several numerical tests assess the stability of the method and the robustness in solving problems characterized by anisotropies
A residual a posteriori error estimate for the stabilization-free virtual element method
Full text linkIn this work, we present the a posteriori error analysis of Stabilization-Free Virtual Element Methods for the 2D Poisson equation. The absence of a stabilizing bilinear form in the scheme allows to prove the equivalence between a suitably defined error measure and standard residual error estimators, which is not obtained in general for stabilized virtual elements. Several numerical experiments are carried out, confirming the expected behaviour of the estimator in the presence of different mesh types, and robustness with respect to jumps of the diffusion term
Bridges and Calculus
No full textThe workshop’s goal is to describe analytically and numerically the shape
of cables in two types of suspension bridges. As bridges design and construction are emblematic tasks of engineering, we aim to immerse students in the challenges
and responsibilities of engineering
Towards stabilization-free Hybrid High-Order methods for elliptic problems
No full textWe devise and study Hybrid High-Order (HHO) methods in a stabilization-free formulation,
i.e. based on discrete bilinear forms not requiring an additional, explicit stabilization term.
The discretization hinges on newly defined reconstruction operators mapping on polynomial
spaces richer than the ones used in standard HHO literature. Optimal order a priori error
estimates are obtained with the expected HHO convergence rates. The well-posedness of
the discrete scheme is currently only conjectured. Extensive numerical tests are presented,
supporting the stability and robustness of the new methods and shedding a light on future
theoretical developments
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