| Author | Joseph E. Flaherty and Peter K. Moore |
|---|---|
| Title | An HP-Adaptive Method in Space and Time for Parabolic Systems |
| Year | 1993 |
| Abstract | We describe an adaptive method-of-lines hp-refinement algorithm in space and time for one-dimensional vector systems of parabolic partial differential equations. Solutions are calculated using Galerkin's method with a piecewise-polynomial hierarchical basis in space and singly-implicit Runge-Kutta (SIRK) methods in time. A posteriori estimates of the local spatial and temporal discretization error are used with a priori error estimates to control spatial and temporal enrichment. Computational results are used to compare and verify the utility of several variants of the basic hp-refinement procedure. |