OPTIMAL AND PRESSURE-INDEPENDENT L2 VELOCITY ERROR ESTIMATES FOR A MODIFIED CROUZEIX-RAVIART STOKES ELEMENT WITH BDM RECONSTRUCTIONS

作     者：C. Brennecke A. Linke C. Merdon J. Schoberl 

作者机构：Eidgen6ssische Technische Hochschule Ziirich Departement Mathematik Riimistr. 101 8092 Ziirich Switzerland Weierstrass Institute for Applied Analysis and Stochastics Mohrenstr. 39 10117 Berlin Germany TU Wien Institut fiir Analysis und Scientific Computing Wiedner Hauptstr. 8-10//1011040 Wien Austria 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2015年第33卷第2期

页      面：191-208页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 08[工学] 081104[工学-模式识别与智能系统] 0714[理学-统计学（可授理学、经济学学位）] 070102[理学-计算数学] 0701[理学-数学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 071102[理学-系统分析与集成] 081103[工学-系统工程] 

基　　金：funded in the framoework of the projeft "Macroscopic Modeling of Transport and Reaction Processes in Magnesium-Air-Batteries" under the research initiative "Energy storage" of the German Federal government 

主　　题：Variational crime Crouzeix-Raviart finite element Divergence-free mixed me-thod Incompressible Navier-Stokes equations A priori error estimates. 

摘      要：Nearly all inf-sup stable mixed finite elements for the incompressible Stokes equations relax the divergence constraint. The price to pay is that a priori estimates for the ve- locity error become pressure-dependent, while divergence-free mixed finite elements de- liver pressure-independent estimates. A recently introduced new variational crime using lowest-order Raviart-Thomas velocity reconstructions delivers a much more robust modi- fied Crouzeix-Raviart element, obeying an optimal pressure-independent discrete H1 ve- locity estimate. Refining this approach, a more sophisticated variational crime employing the lowest-order BDM element is proposed, which also allows proving an optimal pressure- independent L2 velocity error. Numerical examples confirm the analysis and demonstrate the improved robustness in the Navier-Stokes case.