A weak Galerkin finite element method on temporal graded meshes for the multi-term time fractional diffusion equations

Toprakseven Ş.

Computers and Mathematics with Applications, cilt.128, ss.108-120, 2022 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 128
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1016/j.camwa.2022.10.012
  • Dergi Adı: Computers and Mathematics with Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, MLA - Modern Language Association Database, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.108-120
  • Anahtar Kelimeler: Caputo derivative, Graded mesh, L1 methods, Stability, The multi-term time fractional diffusion equations, Weak Galerkin finite-element method
  • Yozgat Bozok Üniversitesi Adresli: Evet

Özet

We consider the multi-term time fractional diffusion equation on a bounded convex domain. We analyze the L1 method on a graded mesh in time to compensate for the weak singularity of the solution and a weak Galerkin finite element method in space discretization. The stability analyses are presented for both semi-discrete and fully-discrete schemes and we prove that two schemes are unconditionally stable. Error estimates in L2-norm and a discrete H1 equivalent norm for both schemes are rigorously derived. Further we discuss the optimal spatial order error estimates in L2-norm. Finally, we give some numerical experiments to show the efficiency of the proposed method.