Reduced-basis approximation a posteriori error estimation for parabolic partial differential equations

By Martin A. Grepl. 2005

103 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/ead0606b3d3cc4793374a6c6cad7b60ec27321eb

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Citations in the corpus

Surrogate and reduced-order modeling: a comparison of approaches for large-scale statistical inverse problems [Chapter 7] (2010, methodology): “To address the challenge of sampling a high-dimensional parmeter space to build a reduced basis, the greedy sampling method was introduced in Grepl (2005); Grepl and Patera (2005); Veroy and Patera (2005); Veroy et al. (2003) to adaptively choose samples by finding the location at which the…”
Model Reduction for Large-Scale Systems with High-Dimensional Parametric Input Space (2008, methodology): “It was also combined with a posteriori error estimators for parameterized parabolic PDEs and applied to several optimal control and inverse problems [15, 14].”
CERTIFIED REDUCED BASIS METHODS FOR NONAFFINE LINEAR TIME-VARYING AND NONLINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS (2012, methodology): “We shall consider Euler-Backward for the time integration although higher-order schemes such as Crank-Nicolson can also be readily treated.(17) We refer to Ref.”
Reduced basis methods for partial differential equations with stochastic influences (2013, methodology): “However, it is straightforward to apply the introduced methodology also for instationary problems, as considered for example in [27, 38, 40].”
Reduced Basis Approximation and a Posteriori Error Estimation for Parametrized Parabolic PDEs: Application to Real‐Time Bayesian Parameter Estimation (2010, methodology): “…second part we develop an RB Bayesian framework for parameter estimation which exploits the rapid response and reliability of the certiﬁed reduced basis method; as an example we consider detection and characterization of a delamination crack by transient thermal analysis (Grepl 2005; Starnes 2002).”
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems (2015, unknown): “It was further developed in reduced basis models for elliptic PDEs in [218], the steady incompressible Navier–Stokes equations in [217], and parabolic PDEs in [111, 112].”