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A Second Order Time Accurate Finite Volume Scheme for the Time-Fractional Diffusion Wave Equation on General Nonconforming Meshes

  • Fayssal Benkhaldoun
  • Abdallah BradjiEmail author
Conference paper
  • 16 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11958)

Abstract

SUSHI (Scheme Using Stabilization and Hybrid Interfaces) is a finite volume method has been developed at the first time to approximate heterogeneous and anisotropic diffusion problems. It has been applied later to approximate several types of partial differential equations. The main feature of SUSHI is that the control volumes can only be assumed to be polyhedral. Further, a consistent and stable Discrete Gradient is developed.

In this note, we establish a second order time accurate implicit scheme for the TFDWE (Time Fractional Diffusion-Wave Equation). The space discretization is based on the use of SUSHI whereas the time discretization is performed using a uniform mesh. The scheme is based on the use of an equivalent system of two low order equations. We sketch the proof of the convergence of the stated scheme. The convergence is unconditional. This work is an improvement of [3] in which a first order scheme, whose convergence is conditional, is established.

Keywords

Finite volume Time Fractional Diffusion Wave Equation System Unconditional convergence Second order time accurate 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.LAGAUniversity of Paris 13ParisFrance
  2. 2.UM6PBenguerirMorocco
  3. 3.LMA (Laboratoire de Mathématiques Appliquées) Faculty of SciencesUniversity of AnnabaAnnabaAlgeria

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