Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations

By Jan S. Hesthaven, Anthony T. Patera. 2007

428 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/451c5c30c1e9eb5285a8fe3b2f0018915ff15c3a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Numerical Analysis

In Statistical and Nonlinear Physics

Citations in the corpus

Reduced basis methods for partial differential equations with stochastic influences (2013, methodology): “As already known from the RB a posteriori error analysis of linear output functionals [73], we add a correction term and consider sN,K(μ, ω) := ` (uN,K ;μ, ω)− rRB(p((1)) N,K ;μ, ω) (5.”
The Empirical Interpolation Method (2013, methodology): “It was originally developed to deal with non-affine functions in the Reduced Basis (RB) method [20].”
A general multipurpose interpolation procedure: the magic points (2008, neutral): “We refer to [19] for a general presentation to the reduced basis method.”
Proper Orthogonal Decomposition for Linear-Quadratic Optimal Control (2013, methodology): “The reduced basis (RB) method, as developed in [20, 56] and [32], is one such reduced-order method, where the basis elements correspond to the dynamics of expected control regimes.”
Adaptive reduced basis finite element heterogeneous multiscale method (2013, methodology): “Instead, only a linear combination of a few parameter independent FE solutions needs to be computed for each element of the training set ΞRB, see [11, 12].”
REDUCED BASIS METHOD FOR FINITE VOLUME APPROXIMATIONS OF PARAMETRIZED LINEAR EVOLUTION EQUATIONS (2008, background): “for linear and multilinear cases can be found in [25] or with a larger scope in the recent book [30].”
Certified reduced basis approximation for parametrized partial differential equations and applications (2011, neutral): “4, we can readily develop an a posteriori error bound for sN (μ): by standard arguments [1, 2] |sN (μ)− sN (μ)| ≤ ||`||(XN )′∆N (μ) where |||uN (μ)−uN (μ)|||μ ≤ ∆N (μ) and ∆N (μ) is given by (47).”
POD‐based model reduction with empirical interpolation applied to nonlinear elasticity (2016, background): “A very similar concept with a different strategy to define the subspace can be found in the reduced basis method [6].”
Stabilized reduced basis method for parametrized advection-diffusion PDEs (2014, methodology): “The computations in this work have been performed in Matlab R © software [39] using the MLife (finite elements) library [53] and an enhanced version (co-developed at CMCS, EPFL) of the rbMIT c © library [24, 41].”