September  2008, 10(4): 873-886. doi: 10.3934/dcdsb.2008.10.873

Adaptive Crank-Nicolson methods with dynamic finite-element spaces for parabolic problems

1. 

Department of University College, Yonsei University, Seoul 120-749, South Korea

2. 

Department of Mathematics, Yonsei University, Seoul 120-749

Received  August 2007 Revised  March 2008 Published  August 2008

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.
Citation: Dongho Kim, Eun-Jae Park. Adaptive Crank-Nicolson methods with dynamic finite-element spaces for parabolic problems. Discrete & Continuous Dynamical Systems - B, 2008, 10 (4) : 873-886. doi: 10.3934/dcdsb.2008.10.873
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