Making Functionality More General

The definition for the notion of a "function" is not cast in stone, but depends upon what we adopt as types in our language. With partial equivalence relations (pers) as types in a relational language, we show that the functional relations are precisely those satisfying the simple equation f = f o fu o f, where "o" and "u" are respectively the composition and converse operators for relations. This article forms part of "A calculational theory of pers as types".

An A Posteriori Error Indicator for Discontinuous Galerkin Approximations of Fourth Order Elliptic Problems

We introduce a residual-based a posteriori error indicator for discontinuous Galerkin discretizations of the biharmonic equation with essential boundary conditions. We show that the indicator is both reliable and efficient with respect to the approximation error measured in terms of a natural energy norm, under minimal regularity assumptions. We validate the performance of the indicator within an adaptive mesh refinement procedure and show its asymptotic exactness for a range of test problems.