Analysis of Flux Corrected Transport Schemes for Evolutionary Convection-Diffusion-Reaction Equations
Abhinav Jha, Naveed Ahmed
TL;DR
This paper analyzes the stability and error estimates of flux corrected transport schemes combined with backward Euler for convection-diffusion-reaction equations, supported by numerical validation.
Contribution
It provides the first comprehensive stability and error analysis for both linear and nonlinear FEM-FCT schemes in this context.
Findings
Numerical results confirm theoretical stability predictions.
Error estimates align with observed numerical accuracy.
Analysis applies to both linear and nonlinear schemes.
Abstract
We report in this paper the analysis for the linear and nonlinear version of the flux corrected transport (FEM-FCT) scheme in combination with the backward Euler time-stepping scheme applied to time-dependent convection-diffusion-reaction problems. We present the stability and error estimates for the linear and nonlinear FEM-FCT scheme. Numerical results confirm the theoretical predictions.
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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Computational Fluid Dynamics and Aerodynamics · Differential Equations and Numerical Methods