Garg, Deepika;
Ganesan, Sashikumaar;
(2022)
An overlapping local projection stabilization for Galerkin approximations of Stokes and Darcy flow problems.
Applied Numerical Mathematics
, 171
pp. 106-127.
10.1016/j.apnum.2021.09.001.
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Abstract
An a priori analysis for a generalized local projection stabilized finite element approximation of the Stokes, and the Darcy flow equations are presented in this paper. A first-order conforming PC1 finite element space is used to approximate both the velocity and pressure. It is shown that the stabilized discrete bilinear form satisfies the inf-sup condition in the generalized local projection norm. Moreover, a priori error estimates are established in a mesh-dependent norm as well as in the L2 -norm for the velocity and pressure. The optimal and quasi-optimal convergence properties are derived for the Stokes and the Darcy flow problems. Finally, the derived estimates are numerically validated with appropriate examples.
| Type: | Article |
|---|---|
| Title: | An overlapping local projection stabilization for Galerkin approximations of Stokes and Darcy flow problems |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.apnum.2021.09.001 |
| Publisher version: | https://doi.org/10.1016/j.apnum.2021.09.001 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Finite element method, Stokes problem, Darcy problems, Generalized local projection stabilization, Inf-sup condition, Error estimates |
| 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-pp.ucl.ac.uk/id/eprint/10180785 |
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