Abstract
In this study, we consider a class of non-autonomous time-fractional partial advection–diffusion-reaction equations with Caputo-type fractional derivative. To obtain the numerical solution to the model problem, we apply the non-symmetric interior penalty Galerkin method in space on a uniform mesh and the L1-scheme in time on a graded mesh. It is demonstrated that the computed solution is discretely stable. Superconvergence of error estimates for the proposed method is obtained using the discrete energy-norm. Also, we have applied the proposed method to solve semi-linear problems after linearizing by Newton’s linearization process. The theoretical results are verified through numerical experiments.
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Acknowledgements
The first author thanks IIT Guwahati for helping with the fellowship and providing him with amenities during his research. The authors thank the anonymous referee for reading the work thoroughly and providing their insightful comments and recommendations, which significantly enhanced the presentation.
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SN contributed the approach, the model problem, and helped with the manuscript’s rewriting and editing. SM put the plan into action, obtained the numerical experiments and error analysis, and wrote the manuscript.
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Communicated by Kai Diethelm.
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Maji, S., Natesan, S. Superconvergence analysis of interior penalty discontinuous Galerkin method for a class of time-fractional diffusion problems. Comp. Appl. Math. 43, 133 (2024). https://doi.org/10.1007/s40314-024-02648-z
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DOI: https://doi.org/10.1007/s40314-024-02648-z