Stability and guaranteed error control of approximations to the Monge-Ampère equation
- This paper analyzes a regularization scheme of the Monge–Ampère equation by uniformly elliptic Hamilton–Jacobi–Bellman equations. The main tools are stability estimates in the L∞ norm from the theory of viscosity solutions which are independent of the regularization parameter ε. They allow for the uniform convergence of the solution uε to the regularized problem towards the Alexandrov solution u to the Monge–Ampère equation for any nonnegative Ln right-hand side and continuous Dirichlet data. The main application are guaranteed a posteriori error bounds in the L∞ norm for continuously differentiable finite element approximations of u or uε.
Download full text files
Statistics
Print On Demand
Additional Services
| Author: | Dietmar Gallistl, Ngoc Tien TranGND |
|---|---|
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/109865 |
| Parent Title (German): | Numerische Mathematik |
| Publisher: | Springer Science and Business Media LLC |
| Type: | Article |
| Language: | English |
| Date of first Publication: | 2023/12/07 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2023/12/07 |
| DOI: | https://doi.org/10.1007/s00211-023-01385-5 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Numerische Mathematik | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Latest Publications (not yet published in print): | Aktuelle Publikationen (noch nicht gedruckt erschienen) |
| Licence (German): |  CC-BY 4.0: Creative Commons: Namensnennung (mit Print on Demand) |
