Burman, Erik and Fernández, Miguel A (2009) Finite element methods with symmetric stabilization for the transient convection-diffusion-reaction equation. Computer Methods in Applied Mechanics and Engineering, 198 (33). pp. 2508-2519. ISSN 0045-7825

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Abstract

We consider implicit and semi-implicit time-stepping methods for finite element approximations of singularly perturbed parabolic problems or hyperbolic problems. We are interested in problems where the advection dominates and stability is obtained using a symmetric, weakly consistent stabilization operator in the finite element method. Several A-stable time discretizations are analyzed and shown to lead to unconditionally stable and optimally convergent schemes. In particular, we show that the contribution from the stabilization leading to an extended matrix pattern may be extrapolated from previous time steps, and hence handled explicitly without loss of stability and accuracy. A fully explicit treatment of the stabilization term is obtained under a CFL condition

Item Type:	Article
Schools and Departments:	School of Mathematical and Physical Sciences > Mathematics
Depositing User:	Erik Burman
Date Deposited:	06 Feb 2012 20:09
Last Modified:	12 Jun 2012 12:53
URI:	http://sro.sussex.ac.uk/id/eprint/24366

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