We present a space-time certified reduced basis method for long-time integration of parametrized parabolic equations with quadratic nonlinearity which admit an affine decomposition in parameter but… (More)

We present a Parametrized-Background Data-Weak (PBDW) formulation of the variational data assimilation (state estimation) problem for systems modeled by partial differential equations. The main… (More)

We present a space-time certified reduced basis method for Burgers’ equation over the spatial interval (0, 1) and the temporal interval (0, T ] parametrized with respect to the Peclet number. We… (More)

A high-order Galerkin Least-Squares (GLS) finite element discretization is combined with massively parallel implicit solvers. The stabilization parameter of the GLS discretization is modified to… (More)

We present a hydrodynamic stability theory for incompressible viscous fluid flows based on a space-time variational formulation and associated generalized singular value decomposition of the… (More)

We present a reduced basis method for parametrized partial differential equations certified by a dual-norm bound of the residual computed not in the typical finite-element “truth” space but rather in… (More)

We introduce a Petrov-Galerkin regularized saddle approximation which incorporates a “model” (partial differential equation) and “data” (M experimental observations) to yield estimates for both state… (More)

This report analyzes the behavior of three variants of the dual-weighted residual (DWR) error estimates applied to the p-dependent discretization that results from the BR2 discretization of a… (More)

A high-order Galerkin Least-Squares (GLS) finite element discretization is combined with a Balancing Domain Decomposition by Constraints (BDDC) preconditioner and inexact local solvers to provide an… (More)