This paper was published in 2015, which has beeb cited by 7 until 2016-09-11 12:07:42 CST. https://arxiv.org/abs/1410.0796
Abstact: This paper, as the sequel to previous work, develops numerical schemes for fractional diffusion equations on a two-dimensional finite domain with triangular meshes. We adopt the nodal discontinuous Galerkin methods for the full spatial discretization by the use of high-order nodal basis, employing multivariate Lagrange polynomials defined on the triangles. Stability analysis and error estimates are provided, which shows that if polynomials of degree N are used, the methods are (N+1)-th order accurate for general triangulations. Finally, the performed numerical experiments confirm the optimal order of convergence.