Multiscale and Adaptivity: Modeling, Numerics and Applications
C.I.M.E. Summer School, Cetraro, Italy 2009, Editors: Giovanni Naldi, Giovanni Russo
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Article
Open AccessInterior estimates for the virtual element method
We analyze the local accuracy of the virtual element method. More precisely, we prove an error bound similar to the one holding for the finite element method, namely, that the local
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Article
A HDG Method for Elliptic Problems with Integral Boundary Condition: Theory and Applications
In this paper, we address the study of elliptic boundary value problems in presence of a boundary condition of integral type (IBC) where the potential is an unknown constant and the flux (the integral of the f...
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Chapter
VEM and the Mesh
In this work we report some results, obtained within the framework of the ERC Project CHANGE, on the impact on the performance of the virtual element method of the shape of the polygonal elements of the underl...
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Article
The virtual element method for a minimal surface problem
In this paper we consider the Virtual Element discretization of a minimal surface problem, a quasi-linear elliptic partial differential equation modeling the problem of minimizing the area of a surface subject...
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Chapter and Conference Paper
FETI-DP Preconditioners for the Virtual Element Method on General 2D Meshes
We analyze the performance of a state-of-the-art domain decomposition approach, the Finite Element Tearing and Interconnecting Dual Primal (FETI-DP) method (Toselli and Widlund, Domain decomposition methods—al...
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Article
Local error analysis for the Stokes equations with a punctual source term
The solution of the Stokes problem with a punctual force in source term is not \(H^1 \times \mathbb {L}^2\) ...
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Article
Erratum to: A New Class of Wavelet-Based Metrics for Image Similarity Assessment
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Article
A New Class of Wavelet-Based Metrics for Image Similarity Assessment
In this paper, we propose a new class of image similarity metrics based on a wavelet decomposition. By suitably combining weighted contributions of the different dyadic frequency bands, we define a class of si...
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Article
A New Construction of Boundary Interpolating Wavelets for Fourth Order Problems
In this article we introduce a new mixed Lagrange–Hermite interpolating wavelet family on the interval, to deal with two types (Dirichlet and Neumann) of boundary conditions. As this construction is a slight m...
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Article
BDDC and FETI-DP for the virtual element method
We build and analyze balancing domain decomposition by constraint and finite element tearing and interconnecting dual primal preconditioners for elliptic problems discretized by the virtual element method. We ...
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Article
Analysis of a mesh-dependent stabilization for the three fields domain decomposition method
We consider a stabilized version of the three fields domain decomposition method in the finite element framework, by a variant of the stabilization proposed in [2]. Under fairly general conditions on the meshes a...
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Chapter and Conference Paper
A Modular Registration Algorithm for Medical Images
The aim of this communication is to present the design of a code for image registration based on a modular structure which allows to easily combine and interchange different image models, transformation classe...
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Book
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Chapter
Adaptive Wavelet Methods
Wavelet bases, initially introduced as a tool for signal and image processing, have rapidly obtained recognition in many different application fields. In this lecture notes we will describe some of the interes...
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Article
Analysis of plates on Winkler foundation by wavelet collocation
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Article
Analysis of the fully discrete fat boundary method
The Fat Boundary Method is a method of the Fictitious Domain class, which was proposed to solve elliptic problems in complex geometries with non-conforming meshes. It has been designed to recover optimal conve...
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Book
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Chapter and Conference Paper
Preconditioners for High Order Mortar Methods based on Substructuring
A class of preconditioners for the Mortar Method based on substructuring is studied. We generalize the results of Achdou, Maday and Widlund [1], obtained for the case of order one finite elements, to a wide cl...
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Article
Implementation of the Mortar Method in the Wavelet Context
The paper is concerned with non-conforming wavelet-type discretization of elliptic partial differential equations. In particular it analyzes some implementation issues related to the form of the constraint ope...
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Article
Local boundary estimates for the Lagrange multiplier discretization of a Dirichlet boundary value problem with application to domain decomposition
We give an estimate on the error resulting from approximating the outer normal derivative of the solution of a second-order partial differential equation with the Lagrange multiplier obtained in using the Lagr...
