An Effective Finite Element Method with Singularity Reconstruction for Fractional Convection-diffusion Equation

Analysis and Petrov-Galerkin numerical approximation for variable coefficient two-sided fractional diffusion, advection, reaction equations

“…Despite the aforementioned progress, the corresponding results for the variable coefficient fractional diffusion, advection, reaction equations are largely missing. There exists some recent work on Petrov-Galerkin approximations to two-sided fractional diffusion, reaction equations [15,17], onesided fractional diffusion, advection, reaction equations [8,12,20], and two-sided fractional diffusion, advection, reaction equations [36], all with constant diffusivity coefficients. To the best of our knowledge, the only available result for the Petrov-Galerkin method applied to variable coefficient fractional diffusion problems is [29], in which the weak coercivity in the sense of inf-sup condition was proved for the one-sided variable coefficient fractional diffusion operator, i.e., Lα r with r = 1.…”