Error Estimation for Multi-Stage Runge-Kutta IMEX Schemes

2015/09/29 by Jehanzeb H. Chaudhry, Chaudhry, Jehanzeb H., James B. Collins +3 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #FOS: Mathematics #Magnetic confinement fusion research #Numerical Analysis (math.NA) #Numerical methods for differential equations #Power System Optimization and Stability

paper · pdf · doi:10.48550/arxiv.1509.08576

openalex publication_date 2015/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

Cited by

• Adjoint-based A Posteriori Error Analysis for Semi-explicit Index-1 and Hessenberg Index-2 Differential-Algebraic Equations

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