Higher-Order Linear Finite Element Methods.
HARVARD UNIV CAMBRIDGE MASS DEPT OF MATHEMATICS
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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 1950s, 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
- Theoretical Mathematics