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Finite element methods with symmetric stabilization for the transient convection-diffusion-reaction equation
journal contribution
posted on 2023-06-08, 05:12 authored by Erik Burman, Miguel A FernándezWe 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
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Publication status
- Published
Journal
Computer Methods in Applied Mechanics and EngineeringISSN
0045-7825Publisher
ElsevierExternal DOI
Issue
33Volume
198Page range
2508-2519Department affiliated with
- Mathematics Publications
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- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
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