SIAM Journal on Scientific Computing, Volume 43, Issue 2, Page A1081-A1107, January 2021.
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.

中文翻译：

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最小二乘有限元约简方法

SIAM科学计算杂志，第43卷，第2期，第A1081-A1107页，2021年1月。
我们为最小二乘有限元框架中的参数化线性椭圆偏微分方程（PDE）提供了一种简化的方法。与对有限维（高保真）近似测量误差的估计相反，开发了一种严格而可靠的误差估计，并显示出它相对于PDE的精确解来约束误差。结果表明，最小二乘有限元的一阶公式是关键因素。通过数值示例说明了该方法。