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Regularization procedures of mixed finite element approximations of the stokes problem
Author(s) -
Pierre Roger
Publication year - 1989
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690050307
Subject(s) - stokes problem , finite element method , mathematics , regularization (linguistics) , mixed finite element method , convergence (economics) , element (criminal law) , bubble , mathematical optimization , calculus (dental) , mathematical analysis , computer science , artificial intelligence , medicine , physics , dentistry , parallel computing , political science , law , economics , thermodynamics , economic growth
We propose a theoretical framework for the study of regularization of the Stokes problem. This enables us to perform a general error analysis and to apply it to known schemes as well as to a new one pertaining to the use of the P1‐P1 element. Finally we show that in the P1‐case the theory can also be used to get convergence results for elements obtained by addition of bubble functions, without using the usual mixed finite element machinery.