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Fast Q1 finite element for two-dimensional integral fractional Laplacian

Author

Listed:
  • Yang, Yi
  • Huang, Jin
  • Wang, Yifei
  • Deng, Ting
  • Li, Hu

Abstract

To investigate 2-dimensional integral fractional Laplacian, a fast Q1 finite element method is proposed based on a weighted trapezoidal rule. Different from the very limited existing finite element approximations, the singular integrals are handled numerically, but the rest of integrals can be exactly evaluated. In addition, the entries of stiffness matrix with Toeplitz structure can be efficiently expressed as c2,sh2−γ144w·e with known vectors w and e, where γ∈(2s,2] and 0

Suggested Citation

  • Yang, Yi & Huang, Jin & Wang, Yifei & Deng, Ting & Li, Hu, 2023. "Fast Q1 finite element for two-dimensional integral fractional Laplacian," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    • Handle: RePEc:eee:apmaco:v:443:y:2023:i:c:s0096300322008256
    DOI: 10.1016/j.amc.2022.127757
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    References listed on IDEAS

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    1. Rama Cont & Ekaterina Voltchkova, 2005. "A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models," Post-Print halshs-00445645, HAL.
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