Adaptive finite element method for fractional differential equations using hierarchical matrices

摘要: Abstract A robust and fast solver for the fractional differential equation (FDEs) involving Riesz derivative is developed using an adaptive finite element method. It based on utilization of hierarchical matrices ( H -Matrices) representation stiffness matrix resulting from discretization FDEs. We employ a geometric multigrid method solution algebraic system equations. combine it with algorithm posteriori error estimation. estimation used to deal general-type singularities arising in Through various test examples we demonstrate efficiency high-accuracy numerical even presence singularities. The proposed technique has been verified effectively through fundamental including Riesz, Left/Right Riemann–Liouville and, furthermore, can be readily extended more general equations different boundary conditions low-order terms.