A note on the design of \(hp\)-adaptive finite element methods for elliptic partial differential equations
The design of an automatic mesh modification strategy that is capable of exploiting both local \(h\)- and \(p\)-refinement is studied. The main focus of the paper is to provide a complete account of the design of a fully automatic \(hp\)-adaptive algorithm for the finite element approximation to a one-dimensional reaction-diffusion equation [cf. \textit{P. K. Moore}, Numer. Math. 94, 367--401 (2003; Zbl 1033.65067)]. Some numerical experiments to highlight the practical performance of the proposed \(hp\)-adaptive finite element algorithm are also given.
scientific article; zbMATH DE number 2167969
scientific article