A LEAST-SQUARES FINITE ELEMENT REDUCED BASIS METHOD

被引：0

作者：

Chaudhry, Jehanzeb H. ^{[1
]}

Olson, Luke N. ^{[2
]}

Sentz, Peter ^{[2
]}

机构：

[1] Univ New Mexico, Dept Math, Albuquerque, NM 87131 USA

[2] Univ Illinois, Dept Comp Sci, Urbana, IL 61801 USA

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2021年 / 43卷 / 02期

关键词：

least-squares; finite elements; reduced basis; POSTERIORI ERROR ESTIMATION; PETROV-GALERKIN PROJECTION; NAVIER-STOKES EQUATIONS; EMPIRICAL INTERPOLATION; BASIS APPROXIMATION; BOUNDS;

D O I：

10.1137/20M1323552

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：A1081 / A1107

页数：27

共 50 条

[1] Moving least-squares finite element method
Musivand-Arzanfudi, M.
Hosseini-Toudeshky, H.
[J]. PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART C-JOURNAL OF MECHANICAL ENGINEERING SCIENCE, 2007, 221 (09) : 1019 - 1037
[2] Dual least-squares finite element method with stabilization
Lee, Eunjung
Na, Hyesun
[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2023, 39 (04) : 2975 - 2997
[3] An investigation of the least-squares finite element method in electromagnetism
Kot, J
[J]. COUPLING OF FLUIDS, STRUCTURES AND WAVES IN AERONAUTICS, PROCEEDINGS, 2003, 85 : 251 - 261
[4] Least-squares finite-element lattice Boltzmann method
Li, YS
LeBoeuf, EJ
Basu, PK
[J]. PHYSICAL REVIEW E, 2004, 69 (06):
[5] Least-squares mixed generalized multiscale finite element method
Chen, Fuchen
Chung, Eric
Jiang, Lijian
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2016, 311 : 764 - 787
[6] Least-squares finite element method for ordinary differential equations
Chung, Matthias
Krueger, Justin
Liu, Honghu
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2023, 418
[7] Least-squares mixed finite element method for Sobolev equations
Gu, HM
Yang, DP
[J]. INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2000, 31 (05): : 505 - 517
[8] Finite element methods of least-squares type
Bochev, PB
Gunzburger, MD
[J]. SIAM REVIEW, 1998, 40 (04) : 789 - 837
[9] Discrete least-squares finite element methods
Keith, Brendan
Petrides, Socratis
Fuentes, Federico
Demkowicz, Leszek
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2017, 327 : 226 - 255
[10] The condition of the least-squares finite element matrices
Fried, Isaac
[J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2016, 106 (09) : 760 - 770

← 1 2 3 4 5 →