| Issue |
ESAIM: M2AN
Volume 57, Number 1, January-February 2023
|
|
|---|---|---|
| Page(s) | 107 - 141 | |
| DOI | https://doi.org/10.1051/m2an/2022026 | |
| Published online | 12 January 2023 | |
Optimal convergence rates in L2 for a first order system least squares finite element method
Part I: Homogeneous boundary conditions
Institute for Analysis and Scientific Computing, TU Wien, A-1040 Vienna, Austria
* Corresponding author: maximilian.bernkopf@tuwien.ac.at; maximilian.bernkopf@gmail.com
We analyze a divergence based first order system least squares method applied to a second order elliptic model problem with homogeneous boundary conditions. We prove optimal convergence in the L2(Ω) norm for the scalar variable. Numerical results confirm our findings.
Mathematics Subject Classification: 65N30 / 65N35 / 65N12
Key words: Least squares method / duality argument
© The authors. Published by EDP Sciences, SMAI 2023
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 use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.