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

Burman, Erik (2011) Crank-Nicolson finite element methods using symmetric stabilization with an application to optimal control problems subject to transient advection - diffusion equations. Communications in Mathematical Sciences, 9 (1). pp. 319-329. ISSN 1539-6746

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Abstract

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.

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Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Erik Burman
Date Deposited: 06 Feb 2012 19:09
Last Modified: 09 Jul 2012 12:34
URI: http://sro.sussex.ac.uk/id/eprint/19435
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