Burman, Erik;
Hansbo, Peter;
Larson, Mats;
(2024)
Cut Finite Element Method for Divergence-Free Approximation of Incompressible Flow: A Lagrange Multiplier Approach.
SIAM Journal on Numerical Analysis
, 62
(2)
pp. 893-918.
10.1137/22m1542933.
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Abstract
In this note, we design a cut finite element method for a low order divergence-free element applied to a boundary value problem subject to Stokes’ equations. For the imposition of Dirichlet boundary conditions, we consider either Nitsche’s method or a stabilized Lagrange multiplier method. In both cases, the normal component of the velocity is constrained using a multiplier, different from the standard pressure approximation. The divergence of the approximate velocities is pointwise zero over the whole mesh domain, and we derive optimal error estimates for the velocity and pressures, where the error constant is independent of how the physical domain intersects the computational mesh, and of the regularity of the pressure multiplier imposing the divergence-free condition.
| Type: | Article |
|---|---|
| Title: | Cut Finite Element Method for Divergence-Free Approximation of Incompressible Flow: A Lagrange Multiplier Approach |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1137/22m1542933 |
| Publisher version: | http://dx.doi.org/10.1137/22m1542933 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, compatible finite elements, incompressibility, CutFEM, fictitious domain, Stokes' equations, Lagrange multipliers |
| 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/10191686 |
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