Mixed finite element method for a time-fractional generalized Rosenau-RLW-Burgers equation

Ning Yang; Yang Liu; Ning Yang; Yang Liu

doi:10.3934/math.2025080

AIMS Mathematics

2025, Volume 10, Issue 1: 1757-1778. doi: 10.3934/math.2025080

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Mixed finite element method for a time-fractional generalized Rosenau-RLW-Burgers equation

Ning Yang ,
Yang Liu ^,

School of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021, China

Received: 28 October 2024 Revised: 05 January 2025 Accepted: 14 January 2025 Published: 24 January 2025
MSC : 24A33, 65M60, 65N30

In this article, the time-fractional generalized Rosenau-RLW-Burgers equation is numerically solved, where the generalized BDF2-$ \theta $ is used to discretize the temporal direction, and the mixed finite element method is applied to the spatial direction. The stability of the fully discrete scheme is proven. Finally, the effectiveness of the numerical scheme is verified through some numerical examples, and the singularity of nonsmooth solutions in the initial time layer is effectively resolved by adding the correction term.
- time-fractional generalized Rosenau-RLW-Burgers equation,
- mixed finite element method,
- generalized BDF2-$ \theta $,
- stability,
- correction term,
- weak singularity
Citation: Ning Yang, Yang Liu. Mixed finite element method for a time-fractional generalized Rosenau-RLW-Burgers equation[J]. AIMS Mathematics, 2025, 10(1): 1757-1778. doi: 10.3934/math.2025080

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Abstract

In this article, the time-fractional generalized Rosenau-RLW-Burgers equation is numerically solved, where the generalized BDF2-$ \theta $ is used to discretize the temporal direction, and the mixed finite element method is applied to the spatial direction. The stability of the fully discrete scheme is proven. Finally, the effectiveness of the numerical scheme is verified through some numerical examples, and the singularity of nonsmooth solutions in the initial time layer is effectively resolved by adding the correction term.

References

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