Burman, E;
Ern, A;
(2017)
A nonlinear consistent penalty method weakly enforcing positivity in the finite element approximation of the transport equation.
Computer Methods in Applied Mechanics and Engineering
, 320
pp. 122-132.
10.1016/j.cma.2017.03.019.
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Abstract
We devise and analyze a new stabilized finite element method to solve the first-order transport (or advection–reaction) equation. The method combines the usual Galerkin/Least-Squares approach to achieve stability with a nonlinear consistent penalty term inspired by recent discretizations of contact problems to weakly enforce a positivity condition on the discrete solution. We prove the existence and the uniqueness of the discrete solution. Then we establish quasi-optimal error estimates for smooth solutions bounding the usual error terms in the Galerkin/Least-Squares error analysis together with the violation of the maximum principle by the discrete solution. Numerical examples are presented to illustrate the performances of the method.
| Type: | Article |
|---|---|
| Title: | A nonlinear consistent penalty method weakly enforcing positivity in the finite element approximation of the transport equation |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.cma.2017.03.019 |
| Publisher version: | http://dx.doi.org/10.1016/j.cma.2017.03.019 |
| 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: | Stabilized finite element method; Consistent penalty; Positivity preserving; Transport equation; Discrete maximum principle |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices 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/1555318 |
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