TY - JOUR
T1 - Adaptive Crank-Nicolson methods with dynamic finite-element spaces for parabolic problems
AU - Kim, Dongho
AU - Park, Eun Jae
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2008/11
Y1 - 2008/11
N2 - We construct a posteriori error estimators for approximate solutions of linear parabolic equations. We consider discretizations of the problem by modified discontinuous Galerkin schemes in time and continuous Galerkin methods in space. Especially, finite element spaces are permitted to change at different time levels. Exploiting Crank-Nicolson reconstruction idea introduced by Akrivis, Makridakis & Nochetto [2], we derive space-time a posteriori error estimators of second order in time for the Crank-Nicolson-Galerkin finite element method.
AB - We construct a posteriori error estimators for approximate solutions of linear parabolic equations. We consider discretizations of the problem by modified discontinuous Galerkin schemes in time and continuous Galerkin methods in space. Especially, finite element spaces are permitted to change at different time levels. Exploiting Crank-Nicolson reconstruction idea introduced by Akrivis, Makridakis & Nochetto [2], we derive space-time a posteriori error estimators of second order in time for the Crank-Nicolson-Galerkin finite element method.
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U2 - 10.3934/dcdsb.2008.10.873
DO - 10.3934/dcdsb.2008.10.873
M3 - Article
AN - SCOPUS:57749202892
VL - 10
SP - 873
EP - 886
JO - Discrete and Continuous Dynamical Systems - Series B
JF - Discrete and Continuous Dynamical Systems - Series B
SN - 1531-3492
IS - 4
ER -