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

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