The \(h,p\) and \(h\)-\(p\) version of the finite element method; basis theory and applications
The paper discusses the fundamental aspects of the three versions of the finite element method with the aim to present the most important facts of the methods that are useful for a better understanding of the results obtained. A simple one-dimensional model problem is considered and the \(h\)-, the \(p\)- and the \(h-p\) versions are explained in detail. Results on the optimal grading of the mesh for a best rate of convergence and the ideas of adaptive mesh construction are described. The authors present results on the features of the \(p\)-version when applied to the model problem, and they discuss some theoretical questions about the \(h- p\) version that give some insight into the desirable mesh design for the \(p\)-version. The authors discuss finally the performance of the \(p\)- and the \(h-p\) version for typical elliptic boundary value problems on polygonal domains especially concerning the singularities of the solution.
scientific article; zbMATH DE number 221750