基于双正交系统的薄板样条稳定混合有限元方法
A Stabilized Mixed Finite Element Method for Thin Plate Splines Based on Biorthogonal Systems
AI总结：
提出一种基于双正交系统的稳定混合有限元方法，通过引入光滑梯度作为附加未知量并利用双正交基消除变量，实现薄板样条离散化，并利用梯度恢复算子的超收敛性证明最优先验估计。
摘要：
薄板样条是散乱数据插值和平滑的流行工具。本文提出一种新颖的稳定混合有限元方法用于薄板样条的离散化。混合形式通过引入光滑梯度作为附加未知量得到。使用一对构成双正交系统的光滑梯度和拉格朗日乘子的基，我们可以轻松消除这两个变量（光滑梯度和拉格朗日乘子），得到正定形式。通过利用梯度恢复算子的超收敛性质，证明了最优先验估计。
英文摘要：
The thin plate spline is a popular tool for the interpolation and smoothing of scattered data. In this paper we propose a novel stabilized mixed finite element method for the discretization of thin plate splines. The mixed formulation is obtained by introducing the gradient of the smoother as an additional unknown. Working with a pair of bases for the gradient of the smoother and the Lagrange multiplier which forms a biorthogonal system, we can easily eliminate these two variables (gradient of the smoother and Lagrange multiplier) leading to a positive definite formulation. The optimal a priori estimate is proved by using a superconvergence property of a gradient recovery operator.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
