An estimate of accuracy for interpolant numerical solutions of a PDE problem
<|reference_start|>An estimate of accuracy for interpolant numerical solutions of a PDE problem: In this paper we present an estimate of accuracy for a piecewise polynomial approximation of a classical numerical solution to a non linear differential problem. We suppose the numerical solution U is computed using a grid with a small linear step and interval time Tu, while the polynomial approximation V is an interpolation of the values of a numerical solution on a less fine grid and interval time Tv << Tu. The estimate shows that the interpolant solution V can be, under suitable hypotheses, a good approximation and in general its computational cost is much lower of the cost of the fine numerical solution. We present two possible applications to linear case and periodic case.<|reference_end|>
@article{argentini2004an,
    title={An estimate of accuracy for interpolant numerical solutions of a PDE
  problem},
    author={Gianluca Argentini},
    journal={APPLIED AND INDUSTRIAL MATHEMATICS IN ITALY, Series on Advances in
  Mathematics for Applied Sciences - Vol. 69, World Scientific Company, 2005,
  56 - 64.},
    year={2004},
    archivePrefix={arXiv},
    eprint={cs/0412120},
    primaryClass={cs.NA math-ph math.MP}
}