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Title: Analysis of finite element methods for second order boundary value problems using mesh dependent norms

Abstract

A new approach to the analysis of finite-element methods is presented which is based on C/sup 0/-finite elements for the approximate solution of second-order boundary-value problems in which error estimates are derived directly in terms of two mesh-dependent norms that are closely related to the L/sub 2/ norm and to the second-order Sobolev norm, respectively, and in which there is no assumption of quasi-uniformity on the mesh family. This is in contrast to the usual analysis, in which error estimates are first derived in the first-order Sobolev norm and subsequently are derived in the L/sub 2/ norm in the second-order Sobolev norm--the second-order Sobolev norm estimates being obtained under the assumption that the functions in the underlying approximating subspaces lie in the second-order Sobolev space and that the mesh family is quasi-unform.

Authors:
;
Publication Date:
Research Org.:
Wisconsin Univ., Madison (USA). Mathematics Research Center
OSTI Identifier:
6456041
Alternate Identifier(s):
OSTI ID: 6456041
Report Number(s):
ORO-3443-78
DOE Contract Number:  
EY-76-S-05-3443
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUNDARY-VALUE PROBLEMS; NUMERICAL SOLUTION; MECHANICS; CALCULATION METHODS; COMBUSTION; DIFFERENTIAL EQUATIONS; FINITE ELEMENT METHOD; FLUID MECHANICS; FRACTURES; CHEMICAL REACTIONS; EQUATIONS; FAILURES; OXIDATION; THERMOCHEMICAL PROCESSES 658000* -- Mathematical Physics-- (-1987)

Citation Formats

Babuska, I., and Osborn, J. Analysis of finite element methods for second order boundary value problems using mesh dependent norms. United States: N. p., 1979. Web.
Babuska, I., & Osborn, J. Analysis of finite element methods for second order boundary value problems using mesh dependent norms. United States.
Babuska, I., and Osborn, J. Thu . "Analysis of finite element methods for second order boundary value problems using mesh dependent norms". United States.
@article{osti_6456041,
title = {Analysis of finite element methods for second order boundary value problems using mesh dependent norms},
author = {Babuska, I. and Osborn, J.},
abstractNote = {A new approach to the analysis of finite-element methods is presented which is based on C/sup 0/-finite elements for the approximate solution of second-order boundary-value problems in which error estimates are derived directly in terms of two mesh-dependent norms that are closely related to the L/sub 2/ norm and to the second-order Sobolev norm, respectively, and in which there is no assumption of quasi-uniformity on the mesh family. This is in contrast to the usual analysis, in which error estimates are first derived in the first-order Sobolev norm and subsequently are derived in the L/sub 2/ norm in the second-order Sobolev norm--the second-order Sobolev norm estimates being obtained under the assumption that the functions in the underlying approximating subspaces lie in the second-order Sobolev space and that the mesh family is quasi-unform.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {1979},
month = {2}
}

Technical Report:
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