Error Estimation for Multi-Stage Runge-Kutta IMEX Schemes
This work provides a new error estimation framework for IMEX schemes, benefiting computational scientists who need reliable error control in simulations involving stiff and non-stiff components.
The authors develop accurate a posteriori error estimates for multi-stage IMEX schemes by constructing a nodally equivalent finite element method and applying adjoint-based error estimation, enabling decomposition of error into components from different parts of the method.
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.