论文标题
最小二乘有限元减少了基础方法
A Least-Squares Finite Element Reduced Basis Method
论文作者
论文摘要
我们在最小二乘有限元框架中提供了用于参数化线性椭圆偏微分方程（PDE）的降低基础（RB）方法。开发了严格且可靠的误差估计，并显示出与PDE精确解决方案结合误差，与估计相对于有限维（高保真）近似值的估计误差。结果表明，最小二乘有限元的一阶公式是关键成分。使用数值示例证明该方法。
We present a reduced basis (RB) 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.
