超收敛
残余物
数学
估计员
有限元法
缩小
应用数学
数学优化
鞍点
平均加权残差法
背景(考古学)
先验与后验
水准点(测量)
混合有限元法
算法
几何学
统计
伽辽金法
古生物学
哲学
物理
大地测量学
认识论
生物
热力学
地理
作者
Ignacio Muga,Sergio Rojas,Patrick Vega
摘要
We introduce an adaptive superconvergent finite element method for a class of mixed formulations to solve partial differential equations involving a diffusion term. It combines a superconvergent postprocessing technique for the primal variable with an adaptive finite element method via residual minimization. Such a residual minimization procedure is performed on a local postprocessing scheme, commonly used in the context of mixed finite element methods. Given the local nature of that approach, the underlying saddle point problems associated with residual minimizations can be solved with minimal computational effort. We propose and study a posteriori error estimators, including the built-in residual representative associated with residual minimization schemes; and an improved estimator which adds, on the one hand, a residual term quantifying the mismatch between discrete fluxes and, on the other hand, the interelement jumps of the postprocessed solution. We present numerical experiments in two dimensions using Brezzi–Douglas–Marini elements as input for our methodology. The experiments perfectly fit our key theoretical findings and suggest that our estimates are sharp.
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