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