@article {2019,
	title = {Weighted Reduced Order Methods for Parametrized Partial Differential Equations with Random Inputs},
	journal = {PoliTO Springer Series},
	year = {2019},
	pages = {27-40},
	abstract = {<p>In this manuscript we discuss weighted reduced order methods for stochastic partial differential equations. Random inputs (such as forcing terms, equation coefficients, boundary conditions) are considered as parameters of the equations. We take advantage of the resulting parametrized formulation to propose an efficient reduced order model; we also profit by the underlying stochastic assumption in the definition of suitable weights to drive to reduction process. Two viable strategies are discussed, namely the weighted reduced basis method and the weighted proper orthogonal decomposition method. A numerical example on a parametrized elasticity problem is shown.</p>},
	doi = {10.1007/978-3-030-04870-9_2},
	url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85084009379\&doi=10.1007\%2f978-3-030-04870-9_2\&partnerID=40\&md5=446bcc1f331167bbba67bc00fb170150},
	author = {L. Venturi and D. Torlo and F. Ballarin and Gianluigi Rozza}
}
@article {2018,
	title = {Stabilized weighted reduced basis methods for parametrized advection dominated problems with random inputs},
	journal = {SIAM-ASA Journal on Uncertainty Quantification},
	volume = {6},
	year = {2018},
	pages = {1475-1502},
	abstract = {<p>In this work, we propose viable and eficient strategies for stabilized parametrized advection dominated problems, with random inputs. In particular, we investigate the combination of the wRB (weighted reduced basis) method for stochastic parametrized problems with the stabilized RB (reduced basis) method, which is the integration of classical stabilization methods (streamline/upwind Petrov-Galerkin (SUPG) in our case) in the ofine-online structure of the RB method. Moreover, we introduce a reduction method that selectively enables online stabilization; this leads to a sensible reduction of computational costs, while keeping a very good accuracy with respect to high-fdelity solutions. We present numerical test cases to assess the performance of the proposed methods in steady and unsteady problems related to heat transfer phenomena.</p>},
	doi = {10.1137/17M1163517},
	url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85058246502\&doi=10.1137\%2f17M1163517\&partnerID=40\&md5=6c54e2f0eb727cb85060e988486b8ac8},
	author = {D. Torlo and F. Ballarin and Gianluigi Rozza}
}
