Adaptive Computational Methods for Parabolic Problems
Kenneth A. Eriksson, Claes Johnson, Anders Logg · 2004
Abstract We present a unified methodology for the computational solution of parabolic systems of differential equations with adaptive selection of discretization in space and time, based on a posteriori error estimates involving residuals of computed solutions and stability factors/weights, obtained by solving an associated linearized dual problem. We define parabolicity as boundedness in time (up to logarithmic factors) of a certain strong stability factor measuring the L 1 ( L 2 )‐norm in time–space of the time derivative of the dual solution with L 2 ‐normalized initial data.