Conclusions and Future Work
The material presented in the two volumes of this monograph summarizes almost two decades of our research on hp methods. We have developed what we believe to be a unique three-dimensional finite element technology. Our major accomplishments include:
On the theory side: the concept of compatible H1-, H(curl)-, and H(div)- conforming hp discretizations based on the exact polynomial sequences for elements of variable order, and the projection-based (PB) interpolation theory. Many of the underlying theoretical results are very technical and have only been mentioned in this monograph.