A Mixed Finite Element Method for the Multi-Term Time-Fractional Reaction–Diffusion Equations

Autor:	Jie Zhao, Shubin Dong, Zhichao Fang
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	multi-term time-fractional reaction–diffusion equations mixed finite element method L1 formula unconditional stability error estimate Thermodynamics QC310.15-319 Mathematics QA1-939 Analysis QA299.6-433
Zdroj:	Fractal and Fractional, Vol 8, Iss 1, p 51 (2024)
Druh dokumentu:	article
ISSN:	2504-3110
DOI:	10.3390/fractalfract8010051
Popis:	In this work, a fully discrete mixed finite element (MFE) scheme is designed to solve the multi-term time-fractional reaction–diffusion equations with variable coefficients by using the well-known L1 formula and the Raviart–Thomas MFE space. The existence and uniqueness of the discrete solution is proved by using the matrix theory, and the unconditional stability is also discussed in detail. By introducing the mixed elliptic projection, the error estimates for the unknown variable u in the discrete L∞(L2(Ω)) norm and for the auxiliary variable λ in the discrete L∞((L2(Ω))2) and L∞(H(div,Ω)) norms are obtained. Finally, three numerical examples are given to demonstrate the theoretical results.
Databáze:	Directory of Open Access Journals
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