Space-Time PetrovGalerkin FEM for Fractional Diffusion Problems Academic Article uri icon

abstract

  • Abstract We present and analyze a space-time PetrovGalerkin finite element method for a time-fractional diffusion equation involving a RiemannLiouville fractional derivative of order ( 0 , 1 ) {alphain(0,1)} in time and zero initial data. We derive a proper weak formulation involving different solution and test spaces and show the inf-sup condition for the bilinear form and thus its well-posedness. Further, we develop a novel finite element formulation, show the well-posedness of the discrete problem, and derive error bounds in both energy and L 2 {L^{2}} norms for the finite element solution. In the proof of the discrete inf-sup condition, a certain nonstandard L 2 {L^{2}} stability property of the L 2 {L^{2}} projection operator plays a key role. We provide extensive numerical examples to verify the convergence analysis.

published proceedings

  • Computational Methods in Applied Mathematics

altmetric score

  • 0.25

author list (cited authors)

  • Duan, B., Jin, B., Lazarov, R., Pasciak, J., & Zhou, Z.

citation count

  • 13

complete list of authors

  • Duan, Beiping||Jin, Bangti||Lazarov, Raytcho||Pasciak, Joseph||Zhou, Zhi

publication date

  • January 2018