Search results for "Simo"
showing 10 items of 459 documents
Quantitative Approximation Properties for the Fractional Heat Equation
2017
In this note we analyse \emph{quantitative} approximation properties of a certain class of \emph{nonlocal} equations: Viewing the fractional heat equation as a model problem, which involves both \emph{local} and \emph{nonlocal} pseudodifferential operators, we study quantitative approximation properties of solutions to it. First, relying on Runge type arguments, we give an alternative proof of certain \emph{qualitative} approximation results from \cite{DSV16}. Using propagation of smallness arguments, we then provide bounds on the \emph{cost} of approximate controllability and thus quantify the approximation properties of solutions to the fractional heat equation. Finally, we discuss genera…
Optimal C∞-approximation of functions with exponentially or sub-exponentially integrable derivative
2023
On O(h[sup4])-superconvergence of piecewise bilinear FE-approximations
1987
On optimal shape design of systems governed by mixed Dirichlet-Signorini boundary value problems
1983
On some partial data Calderón type problems with mixed boundary conditions
2021
In this article we consider the simultaneous recovery of bulk and boundary potentials in (degenerate) elliptic equations modelling (degenerate) conducting media with inaccessible boundaries. This connects local and nonlocal Calderón type problems. We prove two main results on these type of problems: On the one hand, we derive simultaneous bulk and boundary Runge approximation results. Building on these, we deduce uniqueness for localized bulk and boundary potentials. On the other hand, we construct a family of CGO solutions associated with the corresponding equations. These allow us to deduce uniqueness results for arbitrary bounded, not necessarily localized bulk and boundary potentials. T…
Approximation of heat equation and backward SDEs using random walk : convergence rates
2018
This thesis addresses questions related to approximation arising from the fields of stochastic analysis and partial differential equations. Theoretical results regarding convergence rates are obtained by using discretization schemes where the limiting process, the Brownian motion, is approximated by a simple discrete-time random walk. The rate of convergence is derived for a finite-difference approximation of the solution of a terminal value problem for the backward heat equation. This weak approximation result is proved for a terminal function which has bounded variation on compact sets. The sharpness of the according rate is achieved by applying some new results related to the first exit time …
Functional Type Error Control for Stabilised Space-Time IgA Approximations to Parabolic Problems
2018
The paper is concerned with reliable space-time IgA schemes for parabolic initial-boundary value problems. We deduce a posteriori error estimates and investigate their applicability to space-time IgA approximations. Since the derivation is based on purely functional arguments, the estimates do not contain mesh dependent constants and are valid for any approximation from the admissible (energy) class. In particular, they imply estimates for discrete norms associated with stabilised space-time IgA approximations. Finally, we illustrate the reliability and efficiency of presented error estimates for the approximate solutions recovered with IgA techniques on a model example. peerReviewed
A posteriori error estimates for variational problems in the theory of viscous fluids
2016
The papers included in the thesis are focused on functional type a posteriori error estimates for the Stokes problem, the Stokes problem with friction type boundary conditions, the Oseen problem, and the anti-plane Bingham problem. In the summary of the thesis we consider only the Oseen problem. The papers present and justify special forms of these estimates which are suitable for the approximations generated by the Uzawa algorithm. The estimates are of two main types. Estimates of the first type use exact solutions obtained on the steps of the Uzawa algorithm. They show how errors encompassed in Uzawa approximations behave and have mainly theoretical meaning. Estimates of the second type o…
Ancora sul paesaggio ...
2021
Il Paesaggio è una straordinaria e potente fonte di conoscenza e di informazioni sui luoghi perché contiene le tracce di tutte le trasformazioni che quei luoghi hanno subito, nel tempo, per opera della natura e dell’uomo; ha natura concettuale ancorché sostanziato da elementi fisici; è la sintesi dell’osservazione, descrizione e rappresentazione di un luogo attraverso lo scambio tra i processi che regolano identità e identificazione. Un luogo può essere rappresentato in molti modi e, quindi, può produrre più paesaggi. I luoghi si trasformano e, di conseguenza, si trasformano anche i paesaggi. Dunque, parlare di unicità del paesaggio e, ancor di più, di conservazione del paesaggio è un ossim…
Ambiente e clima della Sicilia durante gli ultimi 20 mila anni
2010
Environment and Climate in Sicily over the last 20, 000 years. (IT ISSN 0394-3356, 2010). A series of recent studies shed light on the central Mediterranean, and Sicily, climate and environment, starting from the last glacial maximum (about 20 ka cal BP). In the present paper, we examine most of these works, in order to unravel environmental changes of the past, mainly in terms of temperature, atmospheric pattern, precipitation, vegetation and faunal associations. The climate of the last glacial maximum was characterised by very low temperature and by repeated northerlies penetration, even during summer. Low precipitation values led to a steppe- or semisteppe-like vegetation pattern, domina…