发表机构
Universität Jena（耶拿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为鞍点问题提出转置方法框架，允许标准Galerkin逼近处理更一般数据，涵盖拉普拉斯、Stokes、线弹性、双拉普拉斯及Maxwell问题。
AI 中文摘要
转置方法已知于二阶椭圆偏微分方程理论，本文在满足Brezzi分裂的特定结构假设以及反映具体微分算子带边界条件时椭圆正则性的映射性质下，将其公式化用于鞍点问题。我们设计了一个框架，允许通过标准的、未经修改的Galerkin型方法进行逼近，这些方法相对于转置算子所允许的更一般数据可能是非协调的。数据无需正则化是鞍点方法特有的优势。该框架涵盖的示例包括拉普拉斯算子、Stokes算子、线弹性、双拉普拉斯算子以及具有$L^2$边界数据的稳态Maxwell问题。
英文摘要
The transposition method known from the theory of second-order elliptic partial differential equations is formulated for saddle-point problems under certain structural assumptions known from the Brezzi splitting plus mapping properties that reflect elliptic regularity in concrete instances of differential operators with boundary conditions. A framework is devised that grants approximation by standard, unmodified Galerkin-type methods, which may be nonconforming with respect to the more general data allowed by the transposed operator. That the data need not be regularized is an advantage particular to the saddle-point approach. Examples covered by the framework include the Laplacian, the Stokes operator, linear elasticity, the bi-Laplacian, and the stationary Maxwell problem with $L^2$ boundary data.
