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The stability of finite element methods
Author(s) -
Verfürth Rüdiger
Publication year - 1995
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.1690110108
Subject(s) - finite element method , mathematics , stability (learning theory) , mixed finite element method , norm (philosophy) , convergence (economics) , multigrid method , finite element limit analysis , hp fem , extended finite element method , mathematical analysis , calculus (dental) , partial differential equation , computer science , structural engineering , engineering , medicine , dentistry , machine learning , law , political science , economics , economic growth
We give an abstract stability result for finite element methods. It provides a general guideline for establishing the stability of finite element methods for a given norm once it is established with respect to another norm. The abstract result yields stability estimates of natural norms for finite element methods, which have recently been developed to stabilize effects like dominant convection, incompressibility constraints, or boundary conditions. These stability results simplify the error analysis of the discretizations and are helpful fin the convergence analysis of multigrid methods for the solution of the corresponding discrete problems. © 1995 John Wiley & Sons, Inc.