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Strathprints serves world leading Open Access research by the University of Strathclyde, including research by the Strathclyde Institute of Pharmacy and Biomedical Sciences (SIPBS), where research centres such as the Industrial Biotechnology Innovation Centre (IBioIC), the Cancer Research UK Formulation Unit, SeaBioTech and the Centre for Biophotonics are based.

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An analysis of stability and convergence of a finite-difference discretization of a model parabolic PDE in 1D using a moving mesh

MacKenzie, J.A. and Mekwi, W. (2007) An analysis of stability and convergence of a finite-difference discretization of a model parabolic PDE in 1D using a moving mesh. IMA Journal of Numerical Analysis, 27 (3). pp. 507-528. ISSN 0272-4979

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Abstract

The aim of this paper is to investigate the stability and convergence of time integration schemes for the solution of a semi-discretization of a model parabolic problem in 1D using a moving mesh. The spatial discretization is achieved using a second-order central finite-difference scheme. Using energy techniques we show that the backward Euler scheme is unconditionally stable in a mesh-dependent L2-norm, independently of the mesh movement, but the Crank-Nicolson (CN) scheme is only conditionally stable. By identifying the diffusive and anti-diffusive effects caused by the mesh movement, we devise an adaptive {theta}-method that is shown to be unconditionally stable and asymptotically second-order accurate. Numerical experiments are presented to back up the findings of the analysis.