A high-order global spatially adaptive collocation method for 1-D parabolic PDEs Original Research Article

In this paper, we describe a high-order solver, adaptive in space and time, for the efficient numerical solution of one-dimensional parabolic PDEs. Collocation at Gaussian points is employed for the spatial discretization, using a B-spline basis. A modification of the well-known DAE solver, DASSL is used for the time integration. An a posteriori spatial error estimate is calculated at each successful time step. A new mesh selection strategy based on an equidistribution principle is presented for controlling the spatial error which is balanced with respect to the temporal error. This new mesh adaptation algorithm is shown to be robust, and particularly efficient for problems having solutions with rapid variation.