Abstract
In this paper, an implicit fully discrete direct discontinuous Galerkin (DDG) finite element method is considered for solving the time fractional diffusion equation. The scheme is based on the Gorenflo–Mainardi–Moretti–Paradisi (GMMP) scheme in time and direct discontinuous Galerkin method in space. Unlike the traditional local discontinuous Galerkin method, the DDG method is based on the direct weak formulation for solutions of parabolic equations in each computational cell, letting cells communicate via the numerical flux ux^ only. We prove that our scheme is stable and the energy norm error estimate is convergent with O((Δx)k+Δtα+1+Δtα2(Δx)k) by choosing admissible numerical flux. The DDG method has the advantage of easier formulation and implementation as well as the high order accuracy. Finally numerical experiments are presented to verify our theoretical findings.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
