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Summary: On the norm of the hyperinterpolation operator
on the unit disk and its use for the solution of
the nonlinear Poisson equation
Olaf Hansen
Department of Mathematics
California State University San Marcos
Kendall Atkinson
Departments of Mathematics & Computer Science
The University of Iowa
David Chien
Department of Mathematics
California State University San Marcos
December 6, 2007
Abstract
In this article we study the properties of the hyperinterpolation opera-
tor on the unit disk D in R2
. We show how the hyperinterpolation can be
used in connection with the Kumar-Sloan method to approximate the so-
lution of a nonlinear Poisson equation on the unit disk (discrete Galerkin
method). A bound for the norm of the hyperinterpolation operator in the
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