Analysis of optimal finite element meshes in R/sup 1/
A theory of a posteriori estimates for the finite element method has been developed. On the basis of this theory, for a two-point boundary-value problem the existence of a unique optimal mesh distribution is proved and its properties are analyzed. This mesh is characterized in terms of certain, easily computable local error indicators which in turn allow for a simple adaptive construction of the mesh and also permit the computation of a very effective a posteriori error bound. While the error estimates are asymptotic in nature, numerical experiments show the results to be excellent already for 10% accuracy. The approaches are not restricted to the model problem considered here only for clarity; in fact, they allow for rather straightforward extensions to more general problems in one dimension as well as to higher-order elements. 11 tables.
- Research Organization:
- Maryland Univ., College Park (USA). Inst. for Physical Science and Technology
- OSTI ID:
- 6819687
- Report Number(s):
- ORO-3443-69
- Country of Publication:
- United States
- Language:
- English
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