1,721,226 research outputs found
A new marking strategy for the adaptive finite element approximation of optimal control constrained problems
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A posteriori error estimates for the monodomain model in cardiac electrophysiology
Full text linkWe consider the monodomain model, a system of a parabolic semilinear reaction-diffusion equation coupled with a nonlinear ordinary differential equation, arising from the (simplified) mathematical description of the electrical activity of the heart. We derive a posteriori error estimators accounting for different sources of error (space/time discretization and linearization). We prove reliability and efficiency (this latter under a suitable assumption) of the error indicators. Finally, numerical experiments assess the validity of the theoretical results
The Rhie-Chow stabilized Box Method for the Stokes problem
Full text linkThe Finite Volume method (FVM) is widely adopted in many different applications because of its built-in conservation properties, its ability to deal with arbitrary mesh and its computational efficiency. In this work, we consider the Rhie-Chow stabilized Box Method (RCBM) for the approximation of the Stokes problem. The Box Method (BM) is a piecewise linear Petrov-Galerkin formulation on the Voronoi dual mesh of a Delaunay triangulation, whereas the Rhie-Chow (RC) stabilization is a well known stabilization technique for FVM. The first part of the paper provides a variational formulation of the RC stabilization and discusses the validity of crucial properties relevant for the well-posedeness and convergence of RCBM. Moreover, a numerical exploration of the convergence properties of the method on 2D and 3D test cases is presented. The last part of the paper considers the theoretically justification of the well-posedeness of RCBM and the experimentally observed convergence rates. This latter justification hinges upon suitable assumptions, whose validity is numerically explored.27 pages, 6 figures, 4 table
A multigrid algorithm for the p -version of the virtual element method
Full text linkWe present a multigrid algorithm for the solution of the linear systems of equations stemming from the p-version of the virtual element discretization of a two-dimensional Poisson problem. The sequence of coarse spaces are constructed decreasing progressively the polynomial approximation degree of the virtual element space, as in standard p-multigrid schemes. The construction of the interspace operators relies on auxiliary virtual element spaces, where it is possible to compute higher order polynomial projectors. We prove that the multigrid scheme is uniformly convergent, provided the number of smoothing steps is chosen sufficiently large. We also demonstrate that the resulting scheme provides a uniform preconditioner with respect to the number of degrees of freedom that can be employed to accelerate the convergence of classical Krylov-based iterative schemes. Numerical experiments validate the theoretical results
Valenze ambientali ed economiche dei ravaneti delle Alpi Apuane (Toscana, Italia)
No full textThe Apuan Alps, in Northern Tuscany, are a mainly calcareous-metamorphic range where quarrying is particularly extensive, due to the abundance, quality and beauty of the marble (the Carrara marble is of worldwide renown). In this mountain range geological heritages, or geosites, are widely represented. These include surface and underground karst features, features of Quaternary glaciations and also the particular alpine-type morphology (sharp peaks, steep slopes, deeply cut valleys). Signs of the age-old quarrying activities are also evident. Among these, the accumulation of rock fragments in quarry dumps - locally named ravaneti - is typical of the Apuan Alps and is one of its most important characteristics. The ravaneti result from marble excavation and cover a large surface area of quarried zones. They are the result of an extensive quarrying method, with extensive use of mines, now obsolete and replaced by more up-to-date techniques. At present the ravaneti are taken into consideration from two opposing points of view, that is their environmental and economic-productive relevance. However, both viewpoints must find an accordance with each other.
Indeed, over the last few years, these quarry dumps have been increasingly used as a source of inert materials and calcium carbonate, without any planning or regulation. By contrast, the environmental value of the ravaneti is scarcely taken into consideration, even though they have become an integral part of the Apuan landscape: their whiteness seen in the distance makes the mountainous massif even more particular. Moreover, the ravaneti, which resulted from ancient quarrying techniques, are an important indication of past extractive activity. They sometimes still show traces of quarrying work (e.g. the vie di lizza - rocky chutes once used by quarry workers for sliding marble blocks downslope -, the fragment retaining constructions and the ramps going up to the quarries). They are therefore important features of local industrial archaeology. Finally, the quarry dumps are very large and very pervious. They therefore slow down the rainwater concentration in the watercourses, thereby helping to protect inhabited centres against floods and contributing to aquifer replenishment. This is an important fact in favour of maintenance of the ravaneti . The present market trends lead to the fear that the intensive re-utilization of the ravaneti may become uncontrolled. This has certainly been the case of the indiscriminate quarrying activity in the Apuan Alps over the centuries. We believe it is essential to promote as soon as possible a series of studies, to determine which ravaneti deserve protection from indiscriminate re-utilization. Any selection criteria, based on thematic maps and project files, should consider classification parameters, including: scenic significance, morphology, characteristics of plant adaptation, historical and anthropic value. Even if the introduction of regulatory measures restrict the exploitation of a certain number of ravaneti, millions and millions tons of rock fragments will remain for market use. Moreover, such protective action will raise the tourist value of the area. In conclusion, no damage to the economy of the Apuan district is expected from the adoption of a rational policy for safeguarding the environment
Quarrying activities and geosites of the Apuan Alps (north-western Tuscany, Italy): coexistence possibilities and protection criteria
No full textThe Apuan Alps are a mainly calcareous-metamorphic range in Northern Tuscany that attains the height of ca. 2.000 m above sea level; they imposingly rise on the coastal plain of Versilia, along the Ligurian-Tirrenian Sea. On account of some peculiarities, the whole range, where a Regional Park was established in 1985, may be regarded as a geological heritage, or geosite, of particular environmental value; we refer, for example, to its “alpine” type morphology, characterized by sharp peaks, steep slopes and deeply cut valleys, that make the Apuan Alps very different from the adjacent main chain of the Apennines. Also relevant - and of still greater ambient importance - is the landscape which in a short distance grades from sharp white marble peaks to the coastal plain. There are also specific geosites, related to particular geological, geomorphological or environmental aspects. Among them, the following must be mentioned: surface and underground karst features (Antro del Corchia is among the widest cave system in Europe), such erosive phenomena as pot-holes and ancient glacial evidences, mainly cirques and moraines. By contrast, a marble quarrying activity has been in operation in the Apuan Alps for more than twenty centuries; it often interfered with some of the geosites. This interference resulted either in the destruction of the geosites, or in an important landscape modification due to the quarry excavation itself and the accumulation of marble fragments in quarry dumps (locally called “ravaneti ”). Moreover, the pollution of water supplies contributes to the alteration of natural conditions. With regard to ravaneti, their role is particularly complex; while changing the physical reality, in particular cases their intimate connection with the landscape raises ravaneti to the rank of geosites. So they, or at least the most important of them, become elements to be defended from reworking, through excavation of inert materials, a possibility frequently proposed today. Since the present legislation does not guarantee effective environmental protection, safeguard criteria must be sought and established, which may permit the coexistence of a productive industry, like quarrying, with the safeguard of geosites. The imminent drafting of the “Park Plan”, which should specify the areas to be used as a “total reservation”, appears to be the operational moment. This phase of territorial planning will start with a census of existing geosites, to be followed by the sanctioning of a set of obligations, aimed at protecting the identified geosites.
In fact, only a global safeguard policy will contribute to the preservation of “landscape” and “environment” resources, as vital for the Apuan area as the economically important marble industry
Attualità e innovazione nella gestione del rischio biologico occupazionale negli impianti di depurazione
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