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Preface to the English Edition ix

mathematical textbook. References to textbooks specialised in the topics
of Chapters 4, 5 and 8 are given there.

Remarks on the Notation
Printing in italics emphasizes definitions of notation, even if this is not
carried out as a numbered definition.
Vectors appear in different forms: Besides the “short” space vectors
d
m
x ∈ R there are “long” representation vectors u ∈ R , which describe
in general the degrees of freedom of a finite element (or volume) approxi-
mation or represent the values on grid points of a finite difference method.
Here we choose bold type, also in order to have a distinctive feature from
the generated functions, which frequently have the same notation, or from
the grid functions.
Deviations can be found in Chapter 0, where vectorial quantities belong-
d
ing to R are boldly typed, and in Chapters 5 and 8, where the unknowns
of linear and nonlinear systems of equations, which are treated in a general
m
manner there, are denoted by x ∈ R .
Components of vectors will be designated by a subindex, creating a
double index for indexed quantities. Sequences of vectors will be supplied
with a superindex (in parentheses); only in an abstract setting do we use
subindices.
Erlangen, Germany Peter Knabner
Clausthal-Zellerfeld, Germany Lutz Angermann
January 2002