Finite element approximation of fractional order elliptic boundary value problems

A finite element numerical method is investigated for fractional order elliptic boundary value problems with homogeneous Dirichlet type boundary conditions. It is pointed out that an appropriate stiffness matrix can be obtained by taking the prescribed fractional power of the stiffness matrix corresponding to the non-fractional elliptic operators. It is proved that this approach, which is also called the matrix transformation or matrix transfer method, delivers optimal rate of convergence in the L2L2-norm.