Osborne, Yohance AP;
Smears, Iain;
Wells, Harry;
(2025)
A posteriori error bounds for finite element
approximations of steady-state mean field games.
IMA Journal of Numerical Analysis
, Article draf107. 10.1093/imanum/draf107.
(In press).
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Abstract
We analyze a posteriori error bounds for stabilized finite element discretizations of second-order steady-state mean field games. We prove the local equivalence between the $H^1$-norm of the error and the dual norm of the residual. We then derive reliable and efficient estimators for a broad class of stabilized first-order finite element methods. We also show that in the case of affine-preserving stabilizations, the estimator can be further simplified to the standard residual estimator. Numerical experiments illustrate the computational gains in efficiency and accuracy from the estimators in the context of adaptive methods.
| Type: | Article |
|---|---|
| Title: | A posteriori error bounds for finite element approximations of steady-state mean field games |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1093/imanum/draf107 |
| Publisher version: | https://doi.org/10.1093/imanum/draf107 |
| Language: | English |
| Additional information: | © The Author(s) 2025. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. |
| Keywords: | Mean field games, finite element methods, a posteriori analysis, stabilised methods |
| 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/10212716 |
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