Item request has been placed! ×
Item request cannot be made. ×
loading  Processing Request

Optimal error analysis of a non-uniform IMEX-L1 finite element method for time fractional PDEs and PIDEs

Item request has been placed! ×
Item request cannot be made. ×
loading   Processing Request
اقرأ أكثر حفظ في قائمتي
  • نوع التسجيلة:
    Electronic Resource
  • الدخول الالكتروني :
    http://arxiv.org/abs/2302.05188
  • معلومة اضافية
    • Publisher Information:
      2023-02-10 2023-06-02
    • Added Details:
      Tomar, Aditi
      Tripathi, Lok Pati
      Pani, Amiya K.
    • نبذة مختصرة :
      Stability and optimal convergence analysis of a non-uniform implicit-explicit L1 finite element method (IMEX-L1-FEM) is studied for a class of time-fractional linear partial differential/integro-differential equations with non-self-adjoint elliptic part having (space-time) variable coefficients. The proposed scheme is based on a combination of an IMEX-L1 method on graded mesh in the temporal direction and a finite element method in the spatial direction. With the help of a discrete fractional Gr\"{o}nwall inequality, optimal error estimates in $L^2$- and $H^1$-norms are derived for the problem with initial data $u_0 \in H_0^1(\Omega)\cap H^2(\Omega)$. Under higher regularity condition $u_0 \in \dot{H}^3(\Omega)$, a super convergence result is established and as a consequence, $L^\infty$ error estimate is obtained for 2D problems. Numerical experiments are presented to validate our theoretical findings.
      Comment: 33 pages
    • الموضوع:
      Mathematics - Numerical Analysis; 65M15, 35B65, 65M60; G.1.2; G.1.8; text
    • Other Numbers:
      COO oai:arXiv.org:2302.05188
      1381601045
    • Contributing Source:
      CORNELL UNIV
      From OAIster®, provided by the OCLC Cooperative.
    • الرقم المعرف:
      edsoai.on1381601045
HoldingsOnline