Error Estimation for Multi-Stage Runge-Kutta IMEX Schemes
Numerical Analysis
2016-10-19 v3
Abstract
Implicit-Explicit (IMEX) schemes are widely used for time integration methods for approximating solutions to a large class of problems. In this work, we develop accurate a posteriori error estimates of a quantity of interest for approximations obtained from multi-stage IMEX schemes. This is done by first defining a finite element method that is nodally equivalent to an IMEX scheme, then using typical methods for adjoint-based error estimation. The use of a nodally equivalent finite element method allows a decomposition of the error into multiple components, each describing the effect of a different portion of the method on the total error in a quantity of interest.
Cite
@article{arxiv.1509.08576,
title = {Error Estimation for Multi-Stage Runge-Kutta IMEX Schemes},
author = {Jehanzeb H. Chaudhry and J. B. Collins and John N. Shadid},
journal= {arXiv preprint arXiv:1509.08576},
year = {2016}
}