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Stabilised finite element methods for ill-posed problems with conditional stability

Burman, E; (2016) Stabilised finite element methods for ill-posed problems with conditional stability. In: Barrenechea, GR and Brezzi, F and Cangiani, A and Georgoulis, EH, (eds.) Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations. (pp. pp. 93-127). Springer: Cham, Switzerland. Green open access

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Abstract

In this paper we discuss the adjoint stabilised finite element method introduced in, E. Burman, Stabilized finite element methods for nonsymmetric, noncoercive and ill-posed problems. Part I: elliptic equations, SIAM Journal on Scientific Computing, and how it may be used for the computation of solutions to problems for which the standard stability theory given by the Lax-Milgram Lemma or the Babuska-Brezzi Theorem fails. We pay particular attention to ill-posed problems that have some conditional stability property and prove (conditional) error estimates in an abstract framework. As a model problem we consider the elliptic Cauchy problem and provide a complete numerical analysis for this case. Some numerical examples are given to illustrate the theory.

Type: Proceedings paper
Title: Stabilised finite element methods for ill-posed problems with conditional stability
Event: LMS/EPSRC Symposium "Building bridges: connections and challenges in modern approaches to numerical partial differential equations"
ISBN-13: 978-3-319-41638-0
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/978-3-319-41640-3_4
Publisher version: https://doi.org/10.1007/978-3-319-41640-3_4
Language: English
Additional information: Accepted in the proceedings from the EPSRC Durham Symposium Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/1476745
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