LAUSR

Abstract We analyze finite element approximations to variable-coefficient two-sided space-fractional advection-reaction-diffusion equations in three space dimensions. It is known that the corresponding bilinear form may lose coercivity due to the variable diffusivity coefficient. We prove the weak coercivity of the bilinear form via the Garding's inequality and thus derive the optimal-order error estimate of the finite element method. The developed method is further extended to analyze the time-dependent problems. Numerical experiments are given to validate the theoretical findings.