Analysis of Finite Element Methods for Second Order Boundary Value Problems Using Mesh Dependent Norms.

Abstract

This paper presents a new approach to the analysis of finite element methods based on C-finite elements for the approximate solution of 2nd order boundary value problems in which error estimates are derived directly in terms of two mesh dependent norms that are closely related to the L2 norm and to the 2nd 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 1st order Sobolev norm and subsequently are derived in the L2 norm and in the 2nd order Sobolev norm - the 2nd order Sobolev norm estimates being obtained under the assumption that the functions in the underlying approximating subspaces lie in the 2nd order Sobolev space and that the mesh family is quasi-uniform. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1979
Accession Number
ADA068902

Entities

People

  • I. Babuška
  • J. Osborn

Organizations

  • University of Wisconsin–Madison

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Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Continuum Mechanics
  • Contrast
  • Differential Equations
  • Equations
  • Finite Element Analysis
  • Mathematical Analysis
  • Mathematics
  • Military Research
  • North Carolina
  • Numerical Analysis
  • United States
  • Universities
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra

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  • Space