论文标题
有条件稳定的不适合PDE的最小二乘求解器
Least squares solvers for ill-posed PDEs that are conditionally stable
论文作者
论文摘要
本文涉及对有条件稳定的不良PDE的最小二乘求解器的设计和分析。最小二乘功能中使用的规范和正则化项由条件稳定性假设的成分确定。然后，我们能够建立一个常规错误，鉴于有条件的稳定性假设，在定性上是最好的，而无需假设数据一致。这些优势的价格是处理双重规范，这些规范会降低以验证合适的INF-SUP稳定性。反过来，这是通过为所有示例场景构造合适的Fortin投影仪来完成的。理论发现通过数值实验说明。
This paper is concerned with the design and analysis of least squares solvers for ill-posed PDEs that are conditionally stable. The norms and the regularization term used in the least squares functional are determined by the ingredients of the conditional stability assumption. We are then able to establish a general error bound that, in view of the conditional stability assumption, is qualitatively the best possible, without assuming consistent data. The price for these advantages is to handle dual norms which reduces to verifying suitable inf-sup stability. This, in turn, is done by constructing appropriate Fortin projectors for all sample scenarios. The theoretical findings are illustrated by numerical experiments.
