论文标题
通过特征值分析，在线性变分问题中计算强制性常数
On Computing Coercivity Constants in Linear Variational Problems Through Eigenvalue Analysis
论文作者
论文摘要
在这项工作中，我们研究了数值近似值与变异问题的强制性常数的收敛性。这些常数是用于减少订单建模的严格误差范围的必不可少的组成部分。将这些边界扩展到相对于精确解决方案的误差，需要了解离散强制性常数的收敛速率。通过将强制性常数表征为自动接合线性算子的光谱值来获得结果；对于几个微分方程，我们表明，固化常数与紧凑型操作员的特征值有关。对于这些应用，通过数值示例得出并验证了收敛速率。
In this work, we investigate the convergence of numerical approximations to coercivity constants of variational problems. These constants are essential components of rigorous error bounds for reduced-order modeling; extension of these bounds to the error with respect to exact solutions requires an understanding of convergence rates for discrete coercivity constants. The results are obtained by characterizing the coercivity constant as a spectral value of a self-adjoint linear operator; for several differential equations, we show that the coercivity constant is related to the eigenvalue of a compact operator. For these applications, convergence rates are derived and verified with numerical examples.
