Comparison of adaptive methods for one-dimensional parabolic systems

Abstract We describe two adaptive space-time hp -refinement algorithms for solving one-dimensional vector systems of parabolic partial differential equations. Solutions for both methods are calculated using Galerkin's method with a piecewise polynomial hierarchical basis in space. The first method, hpsirk , uses singly-implicit Runge-Kutta methods in time and integrates the spatial and temporal discretization strategies. The second, hpdassl , is a method-of-lines approach using a BDF code. The two methods are compared along with the algorithm epdcol as a benchmark on four nonlinear test problems.

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