Finite element methods with symmetric stabilization for the transient convection―diffusion-reaction equation

By Erik Burman, M. Fernández. 2009

53 citations recorded by the source corpus.

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.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/fb3dcdc27fa6d67b9e4c9fe182e258d653ec852b

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In Computational Mechanics

1. Erik Burman
2. Volker John
3. Petr Knobloch
4. Peter Hansbo
5. Alexander Linke
6. Yuri Bazilevs
7. Ronaldo I. Borja
8. Fushen Liu

In Computational Theory and Mathematics

1. Erik Burman
2. Volker John
3. Petr Knobloch
4. Alexander Linke
5. Yuri Bazilevs

In Numerical Analysis

1. Erik Burman

Citations in the corpus

• Consistent SUPG-method for transient transport problems: Stability and convergence (2010, methodology): “Recently a class of symmetric stabilization methods were analyzed with the theta-scheme and the second order backward differentiation scheme, using either an implicit or an explicit treatment of the stabilization term [3].”