Higher-Order Linear Finite Element Methods.

Abstract

During the past decade, a great variety of 'finite element' methods have been developed for reducing boundary value problems, especially those of continuum mechanics, to systems of algebraic equations in a large (100-100,000) but finite number of unknowns. Moreover one can often greatly reduce the number of unknowns needed to achieve a given accuracy by using higher-order (e.g., bicubic spline) approximations. This raises several questions: (1) When are such finite element methods more effective than the difference methods developed in the 1950's, and why. (2) How should one solve the resulting systems of algebraic equations. (3) Which higher-order finite element methods are most efficient, and under what circumstances should they be used. The present report gives some partial answers to these questions for some typical classes of linear problems. (Author)

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1974
Accession Number
AD0779341

Entities

People

  • Garrett Birkhoff
  • George J. Fix

Organizations

  • Harvard University

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Boundaries
  • Boundary Value Problems
  • Continuum Mechanics
  • Differential Equations
  • Equations
  • Finite Element Analysis
  • Mathematics
  • Mechanics

Readers

  • Linear Algebra
  • Structural Dynamics.
  • Systems Analysis and Design