On obtaining higher order convergence for smooth periodic functions

On Weak Convergence of Locally Periodic Functions

We have not found proofs of these facts in the literature. The aim of this paper is to present such proofs. Moreover, we show that the first statement also holds for the case p = 1. The two facts described above are used in the proof of the reiterated homogenization result for monotone operators, see [14] and [15]. The solution uξh is used to define a sequence of functions similar to the ones i...

Deforestation for Higher-Order Functions

Higher Order Functions Considered Unnecessary for Higher Order Programming

It is often claimed that the essence of functional programming is the use of functions as values, i.e., of higher order functions, and many interesting examples have been given showing the power of this approach. Unfortunately, the logic of higher order functions is diicult, and in particular, higher order uniication is undecidable. Moreover (and closely related), higher order expressions are n...

Higher-Order Functions for Parsing

In combinator parsing , the text of parsers resembles BNF notation. We present the basic method, and a number of extensions. We address the special problems presented by white– space, and parsers with separate lexical and syntactic phases. In particular, a combining form for handling the “offside rule” is given. Other extensions to the basic method include an “into” combining form with many use...

On the order of accuracy of the immersed boundary method: Higher order convergence rates for sufficiently smooth problems

The immersed boundary method is both a mathematical formulation and a numerical scheme for problems involving the interaction of a viscous incompressible fluid and a (visco-)elastic structure. In [M.-C. Lai, Simulations of the flow past an array of circular cylinders as a test of the immersed boundary method, Ph.D. thesis, Courant Institute of Mathematical Sciences, New York University, 1998; M...