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arXiv · 1509.08576

Error Estimation for Multi-Stage Runge-Kutta IMEX Schemes

Jehanzeb H. Chaudhry·J. B. Collins·John N. Shadid
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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.

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Jehanzeb H. Chaudhry, J. B. Collins, John N. Shadid. 2015-09-29. Error Estimation for Multi-Stage Runge-Kutta IMEX Schemes. https://arxiv.org/abs/1509.08576

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