Garg, Deepika;
Ganesan, Sashikumaar;
(2022)
Generalized local projection stabilized nonconforming finite element methods for Darcy equations.
Numerical Algorithms
, 89
pp. 341-369.
10.1007/s11075-021-01117-6.
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Abstract
An a priori analysis for a generalized local projection stabilized finite element solution of the Darcy equations is presented in this paper. A first-order nonconforming P nc 1 finite element space is used to approximate the velocity, whereas the pressure is approximated using two different finite elements, namely piecewise constant P0 and piecewise linear nonconforming P nc 1 elements. The considered finite element pairs, P nc 1 /P0 and P nc 1 /P nc 1 , are inconsistent and incompatibility, respectively, for the Darcy problem. The stabilized discrete bilinear form satisfies an inf-sup condition with a generalized local projection norm. Moreover, a priori error estimates are established for both finite element pairs. Finally, the validation of the proposed stabilization scheme is demonstrated with appropriate numerical examples.
| Type: | Article |
|---|---|
| Title: | Generalized local projection stabilized nonconforming finite element methods for Darcy equations |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s11075-021-01117-6 |
| Publisher version: | https://doi.org/10.1007/s11075-021-01117-6 |
| 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 · Darcy flows · Generalized local projection stabilization · Stability · Inf-sup condition · Nonconforming FEM · 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/10180786 |
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