A posteriori Error Estimation for the Spectral Deferred Correction Method
Numerical Analysis
2020-07-07 v2 Numerical Analysis
Abstract
The spectral deferred correction method is a variant of the deferred correction method for solving ordinary differential equations. A benefit of this method is that is uses low order schemes iteratively to produce a high order approximation. In this paper we consider adjoint-based a posteriori analysis to estimate the error in a quantity of interest of the solution. This error formula is derived by first developing a nodally equivalent finite element method to the spectral deferred correction method. The error formula is then split into various terms, each of which characterizes a different component of the error. These components may be used to determine the optimal strategy for changing the method parameters to best improve the error.
Cite
@article{arxiv.2003.03399,
title = {A posteriori Error Estimation for the Spectral Deferred Correction Method},
author = {Jehanzeb H. Chaudhry and J. B. Collins},
journal= {arXiv preprint arXiv:2003.03399},
year = {2020}
}