Adaptive Computational Methods for Parabolic Problems
Book chapter, 2017
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[[inf]]1[[/inf]](L[[inf]]2[[/inf]])-norm in time-space of the time derivative of the dual solution with L[[inf]]2[[/inf]]-normalized initial data.
space-time discretization
convection-diffusion reaction
parabolic
stability factor/weight
a priori error estimate
stiff
a posteriori error estimate
time step control
Galerkin method
finite elements
dual linearized problem
adaptive error control
Author
Kenneth Eriksson
Chalmers, Mathematical Sciences
Anders Logg
Chalmers, Mathematical Sciences, Mathematics
Claes Johnson
Royal Institute of Technology (KTH)
Encyclopedia of Computational Mechanics
1-28
9781119003793 (ISBN)
Subject Categories (SSIF 2025)
Computational Mathematics
Mathematical Analysis
DOI
10.1002/9781119176817.ecm2021