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An Adaptive hp-DG-FE Method for Elliptic Problems: Convergence and Optimality in the 1D Case

Communications on Applied Mathematics and Computation 2019年第3期1卷 309-331页

作者： Paola Antonietti claudio canuto Marco Verani MOX-Dipartimento di Matematica Politecnico di MilanoP.zza Leonardo Da Vinci 3220133 MilanItaly Dipartimento di Scienze Matematiche Politecnico di TorinoCorso Duca degli Abruzzi 2410129 TurinItaly

We propose and analyze an hp-adaptive DG-FEM algorithm, termed hp-ADFEM, and its one-dimensional realization, which is convergent, instance optimal, and h- and p-robust. The procedure consists of iterating two routines:one hinges on Binev's algorithm for the adaptive hp-approximation of a given function, and finds a near-best hp-approximation of the current discrete solution and data to a desired accuracy;the other one improves the discrete solution to a finer but comparable accuracy, by iteratively applying D?rfler marking and h refinement.

关键词： Elliptic problem Discontinuous Galerkin method hp-adaptivity Convergence and optimality

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Numerical Solution of Partial Differential Equations in Random Domains:An Application to Wind Engineering

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Communications in Computational Physics 2009年第2期5卷 515-531页

作者： claudio canuto Davide Fransos Dipartimento di Matematica Politecnico di TorinoC.so Duca degli Abruzzi 2410129 TorinoItaly

An application of recent uncertainty quantification techniques to Wind Engineering is presented.In particular,the study of the effects of small geometric changes in the Sunshine Skyway Bridge deck on its aerodynamic behavior is addressed.This results in the numerical solution of a proper PDE posed in a domain affected by randomness,which is handled through a mapping approach.A non-intrusive Polynomial Chaos expansion allows to transform the stochastic problem into a deterministic one,in which a commercial code is used as a black-box for the solution of a number of Reynolds-Averaged Navier-Stokes simulations.The use of proper Gauss-Patterson nested quadrature formulas with respect to a Truncated Weibull probability density function permits to limit the number of these computationally expensive simulations,though maintaining a sufficient accuracy.Polynomial Chaos approximations,statistical moments and probability density functions of time-independent quantities of interest for the engineering applications are obtained.

关键词： Uncertainty quantification stochastic partial differential equations random domains mapping approach polynomial chaos wind engineering

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