TY - JOUR

T1 - What are C and h?

T2 - Inequalities for the analysis and design of finite element methods

AU - Harari, Isaac

AU - Hughes, Thomas J.R.

N1 - Funding Information:
This research was supported in part by the U.S. Office of Naval Research under Contracts N00014-89-K-0027 and N00014-88-K-0446. The authors are grateful to Leo Franca, whose ongoing interest in this work provided an impetus for its publication.

PY - 1992/6

Y1 - 1992/6

N2 - Increasing mathematical analysis of finite element methods is motivating the inclusion of mesh-dependent terms in new classes of methods for a variety of applications. Several inquualities of functional analysis are often employed in convergence proofs. In the following, Poincaré-Friedrichs inequalities, inverse estimates and least-squares bounds are characterized as tools for the error analysis and practical design of finite element methods with terms that depend on the mesh parameter. Sharp estimates of the constants of these inequalities are provided, and precise definitions of mesh size that arise naturally in the context of different problems in terms of element geometry are derived.

AB - Increasing mathematical analysis of finite element methods is motivating the inclusion of mesh-dependent terms in new classes of methods for a variety of applications. Several inquualities of functional analysis are often employed in convergence proofs. In the following, Poincaré-Friedrichs inequalities, inverse estimates and least-squares bounds are characterized as tools for the error analysis and practical design of finite element methods with terms that depend on the mesh parameter. Sharp estimates of the constants of these inequalities are provided, and precise definitions of mesh size that arise naturally in the context of different problems in terms of element geometry are derived.

UR - http://www.scopus.com/inward/record.url?scp=0026872324&partnerID=8YFLogxK

U2 - 10.1016/0045-7825(92)90162-D

DO - 10.1016/0045-7825(92)90162-D

M3 - מאמר

AN - SCOPUS:0026872324

VL - 97

SP - 157

EP - 192

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0374-2830

IS - 2

ER -