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.
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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 |
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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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