What are C and h? Inequalities for the analysis and design of finite element methods

Isaac Harari, Thomas J.R. Hughes

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)157-192
Number of pages36
JournalComputer Methods in Applied Mechanics and Engineering
Volume97
Issue number2
DOIs
StatePublished - Jun 1992
Externally publishedYes

Fingerprint

Dive into the research topics of 'What are C and h? Inequalities for the analysis and design of finite element methods'. Together they form a unique fingerprint.

Cite this