A probabilistic finite element method based on random meshes: A posteriori error estimators and Bayesian inverse problems
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2020
Mathematical models involving multiple scales are essential for the description of physical systems. In particular, these models are important for the simulation of time-dependent phenomena, such as the heat flow, where the Laplacian contains mixed and ind ...
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This thesis is devoted to the derivation of a posteriori error estimates for the numerical approximation of fluids flows separated by a free surface. Based on these estimates, error indicators are introduced and adaptive algorithms are proposed to solve th ...
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Back analysis can provide engineers with important information for better decision-making. Over the years, research on back analysis has focused mainly on optimisation techniques, while comparative studies of data-interpretation methodologies have seldom b ...
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The present work deals with rational model order reduction methods based on the single-point Least-Square (LS) Padé approximation techniques introduced in Bonizzoni et al. (ESAIM Math. Model. Numer. Anal., 52(4), 1261–1284 2018, Math. Comput. 89, 1229–1257 ...
A novel probabilistic numerical method for quantifying the uncertainty induced by the time integration of ordinary differential equations (ODEs) is introduced. Departing from the classical strategy to randomize ODE solvers by adding a random forcing term, ...
Variational Bayes (VB) methods have emerged as a fast and computationally-efficient alternative to Markov chain Monte Carlo (MCMC) methods for scalable Bayesian estimation of mixed multinomial logit (MMNL) models. It has been established that VB is substan ...
The focus of this work is on the development of an error-driven isogeometric framework, capable of automatically performing an adaptive simulation in the context of second- and fourth-order, elliptic partial differential equations defined on two-dimensiona ...