A saddle point least squares approach for primal mixed formulations of second order PDEs

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• 作者：Constantin Bacuta ; ^{bacuta@udel.edu} ; Klajdi Qirko ^{kqirko@udel.edu}
• 关键词：Least squares ; Saddle point systems ; Mixed methods ; Uzawa type algorithms ; Conjugate gradient ; Dual DPG
• 刊名：Computers & Mathematics with Applications
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：73
• 期：2
• 页码：173-186
• 全文大小：477 K
• 卷排序：73

文摘

We present a Saddle Point Least Squares (SPLS) method for discretizing second order elliptic problems written as primal mixed variational formulations. A stability LBB condition and a data compatibility condition at the continuous level are automatically satisfied. The proposed discretization method follows a general SPLS approach and has the advantage that a discrete inf–sup condition is automatically satisfied for standard choices of the test and trial spaces. For the proposed iterative processes a nodal basis for the trial space is not required. Efficient preconditioning techniques that involve inversion only on the test space can be considered. Stability and approximation properties for two choices of discrete spaces are investigated. Applications of the new approach include discretization of second order problems with highly oscillatory coefficient, interface problems, and higher order approximation of the flux for elliptic problems with smooth coefficients.