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Crank-Nicolson finite element methods using symmetric stabilization with an application to optimal control problems subject to transient advection - diffusion equations

journal contribution
posted on 2023-06-07, 22:07 authored by Erik Burman
We consider a finite element method with symmetric stabilization for transient advection-diffusion-reaction problems. The Crank-Nicolson finite difference scheme is used for discretization in time. We prove stability of the numerical method both for implicit and explicit treatment of the stabilization operator. The resulting convergence results are given and the results are illustrated by a numerical experiment. We then consider a model problem for pde-constrained optimization. Using discrete adjoint consistency of our stabilized method we show that both the implicit and semi-implicit methods proposed yield optimal convergence for the control and the state variable.

History

Publication status

  • Published

Journal

Communications in Mathematical Sciences

ISSN

1539-6746

Publisher

International Press

Issue

1

Volume

9

Page range

319-329

Department affiliated with

  • Mathematics Publications

Notes

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Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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