MATHICSE Technical Report : A posteriori error estimations for elliptic partial differential equations with small uncertainties
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We consider the capacity planning of telecommunications networks with linear investment costs and uncertain future traffic demands. Transmission capacities must be large enough to meet, with a high quality of service (QoS), the range of possible demands, a ...
We consider a method to efficiently evaluate in a real-time context an output based on the numerical solution of a partial differential equation depending on a large number of parameters. We state a result allowing to improve the computational performance ...
Probabilistic programming is a powerful high-level paradigm for probabilistic modeling and inference. We present Odds, a small domain-specific language (DSL) for probabilistic programming, embedded in Scala. Odds provides first-class support for random var ...
We consider goal-oriented a posteriori error estimators for the evaluation of the errors on quantities of interest associated with the solution of geometrically nonlinear curved elastic rods. For the numerical solution of these nonlinear one-dimensional pr ...
The 3DVAR filter is prototypical of methods used to combine observed data with a dynamical system, online, in order to improve estimation of the state of the system. Such methods are used for high dimensional data assimilation problems, such as those arisi ...
We study the single-phase flow in a saturated, bounded heterogeneous porous medium. We model the permeability as a log-normal random field. We perform a perturbation analysis, expanding the solution in Taylor series. The series is directly computable in th ...
We consider oscillators whose parameters randomly switch between two values at equal time intervals. If random switching is fast compared to the oscillator's intrinsic time scale, one expects the switching system to follow the averaged system, obtained by ...
The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the "reduced basis". The purpose of th ...
In this paper Monte Carlo finite element approximations for elliptic homogenization problems with random coefficients, which oscillate on n is an element of N a priori known, separated microscopic length scales, are considered. The convergence of multileve ...
We propose a Reduced Basis method for the solution of parametrized optimal control problems with control constraints for which we extend the method proposed in Dedè, L. (SIAM J. Sci. Comput. 32:997, 2010) for the unconstrained problem. The case of a linear ...