New local discontinuous Galerkin method for a fractional time diffusion wave equation

ABSTRACT

This paper is devoted to the study of a new discontinuous finite element idea for the time fractional diffusion-wave equation defined in bounded domain. The time fractional derivatives are described in the Caputo's sense. By applying the sine transform on the time fractional diffusion-wave equation, we make the equation depend on time. Then we use definition of Caputo's derivative and by defining l-degree discontinuous finite element with interpolated coefficients we solve the mentioned equation. Error estimate, existence and uniqueness are proved. Finally, the theoretical results are tested by some numerical examples.

KEYWORDS:

• Discontinuous finite element method
• fractional order diffusion-wave equation
• finite element method
• error estimate

MATHEMATICS SUBJECT CLASSIFICATION 2010:

• 65M12
• 65M15
• 65M60
• 82D10
• 35L80

Acknowledgements

The authors thank anonymous referee and editor whose constructive comments improved the quality of this paper and finally it is a pleasure to acknowledge the skilful editorial assistance of this journal, Suguna Selvakumar.

Disclosure statement

No potential conflict of interest was reported by the authors.