ABSTRACT
Chapter 2
Hierarchic master elements
of arbitrary order
The rst step in the technology of hierarchic higher-order nite element meth-
ods is to design suitable master elements of arbitrary polynomial order. We
will consider the most commonly used reference domains, equip them with
appropriate scalar and vector-valued polynomial spaces and dene hierarchic
higher-order shape functions. Some of the constructions are actually quite ex-
citing, particularly in vector-valued spaces in higher spatial dimensions, but
in each case this chapter is intended merely as a database of formulae rather
than information for systematic study. The reader may nd it interesting to
read about the De Rham diagram (Section 2.1) which relates the spaces H
,
H(curl), H(div) and L
by means of dierential operators, since nite ele-
ments in these spaces have to respect the diagram as well. Then she/he may
visit a paragraph that discusses a particular nite element of interest.