@article{41e8951f8f9e4af39a2f010a123ecffa,
title = "A least-squares finite element reduced basis method",
abstract = "We present a reduced basis method for parametrized linear elliptic partial differential equations (PDEs) in a least-squares finite element framework. A rigorous and reliable error estimate is developed, and is shown to bound the error with respect to the exact solution of the PDE, in contrast to estimates that measure error with respect to a finite-dimensional (high-fidelity) approximation. It is shown that the first-order formulation of the least-squares finite element is a key ingredient. The method is demonstrated using numerical examples.",
keywords = "Finite elements, Least-squares, Reduced basis",
author = "CHAUDHRY, {JEHANZEB H.} and OLSON, {LUKE N.} and PETER SENTZ",
note = "Funding Information: ∗Submitted to the journal{\textquoteright}s Methods and Algorithms for Scientific Computing section March 5, 2020; accepted for publication (in revised form) November 27, 2020; published electronically March 23, 2021. https://doi.org/10.1137/20M1323552 Funding: The work of the first author was supported by the NSF through grant DMS 1720402. †Department of Mathematics, University of New Mexico, Albuquerque, NM 87131 USA (jehanzeb@unm.edu, https://math.unm.edu/∼jehanzeb). ‡Department of Computer Science, University of Illinois at Urbana Champaign, Urbana, IL 61801 USA (lukeo@illinois.edu, http://lukeo.cs.illinois.edu, sentz2@illinois.edu). Publisher Copyright: {\textcopyright} 2021 Society for Industrial and Applied Mathematics Publications. All rights reserved.",
year = "2021",
doi = "10.1137/20M1323552",
language = "English (US)",
volume = "43",
pages = "A1081--A1107",
journal = "SIAM Journal on Scientific Computing",
issn = "1064-8275",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "2",
}