A nonlinear consistent penalty method weakly enforcing positivity in the finite element approximation of the transport equation

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.
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Computer Methods in Applied Mechanics and Engineering, Elsevier, 2017, 320, pp.122-132. 〈10.1016/j.cma.2017.03.019〉
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Soumis le : vendredi 24 novembre 2017 - 16:59:25
Dernière modification le : mardi 3 juillet 2018 - 11:30:03

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Erik Burman, Alexandre Ern. A nonlinear consistent penalty method weakly enforcing positivity in the finite element approximation of the transport equation. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2017, 320, pp.122-132. 〈10.1016/j.cma.2017.03.019〉. 〈hal-01383295v2〉

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