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

Dongho Kim; Eun-Jae Park

doi:10.3934/dcdsb.2008.10.873

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2008, Volume 10, Issue 4: 873-886. Doi: 10.3934/dcdsb.2008.10.873

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

Dongho Kim^1, and
Eun-Jae Park^2,

1.
Department of University College, Yonsei University, Seoul 120-749
2.
Department of Mathematics, Yonsei University, Seoul 120-749

Received: July 31, 2007

Revised: February 29, 2008

Published: August 2008

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Abstract

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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Mathematics Subject Classification: Primary: 65K10, 65M12, 65M60; Secondary: 76.

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