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Volume 17,     Number 3,     Fall 2009

 

SUPERCONVERGENT INTERPOLANTS FOR
EFFICIENT SPATIAL ERROR ESTIMATION IN
1D PDE COLLOCATION SOLVERS
TOM ARSENAULT, TRISTAN SMITH AND PAUL MUIR

Abstract. This paper considers the use of a superconvergent interpolant (SCI) for spatial error estimation when Gaussian collocation is employed as the spatial discretization scheme in a method-of-lines algorithm for the numerical solution of a system of one-dimensional parabolic partial differential equations (PDEs). Gaussian collocation is a popular approach for the spatial discretization of parabolic PDEs, and at certain points within the problem domain, the collocation solution is superconvergent. This paper describes how an interpolant based on these superconvergent values can be used to provide an efficient error estimate for the collocation solution. We implement this scheme within a modified version of the collocation PDE solver, BACOL. The original BACOL code obtains a spatial error estimate by computing a second global collocation solution of one higher order of accuracy. We show that the SCI based error estimation approach can provide spatial error estimates of comparable accuracy to those currently computed by BACOL, but at a much lower cost.

 

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