No abstract

We derive a high-order compact alternating direction implicit (ADI) method for solving three-dimentional unsteady convection-diffusion problems. The method is fourth-order in space and second-order in time. It permits multiple uses of the one-dimensional tridiagonal algorithm with a considerable saving in computing time and results in a very efficient solver. It is shown through a discrete Fourier analysis that the method is unconditionally stable in the diffusion case. Numerical experiments are conducted to test its high order and to compare it with the standard second-order Douglas-Gunn ADI method and the spatial fourth-order compact scheme by Karaa.

In this paper, a semi-discrete spatial finite volume (FV) method is proposed and analyzed for approximating solutions of anomalous subdiffusion equations involving a temporal fractional derivative of orderis shown to hold. Superconvergence result is proved and as a consequence, it is established that quasioptimal order of convergence in L ∞ (L ∞ ) holds. We also consider a fully discrete scheme that employs FV method in space, and a piecewise linear discontinuous Galerkin method to discretize in temporal direction. It is, further, shown that convergence rate is of order O(h 2 + k 1+α ), where h denotes the space discretizing parameter and k represents the temporal discretizing parameter. Numerical experiments indicate optimal convergence rates in both time and space, and also illustrate that the imposed regularity assumptions are pessimistic.

No abstract

No abstract