Abstract
The hierarchical concept for finite element shape functions was introduced many years ago as a convenient device for mixed order interpolation. Its full advantages have not been realized until a much later time—and these include in addition 1. (a) improved conditioning; 2. (b) ease of introducing error indicators if successive refinement is sought. Further, it is possible to use the ideas to construct a range of error estimators which compare well with alternatives and are ideally suited for adaptive refinements of analysis. As the hierarchical elements are equally simple to implement as “standard” fixed order elements it is felt that more programs will, in the future, turn to utilize their advantages. This is especially true in the field of nonlinear analysis where even today computational economies are necessary.
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