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Error analysis of projection methods for non inf-sup stable mixed finite elements. The Navier-Stokes equations

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Javier de Frutos, Bosco García-Archilla, Julia Novo

Numerical Analysis · Submitted 14 Nov 2016

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove that the modified Euler non-incremental scheme has an inherent stabilization that allows the use of non inf-sup stable mixed finite elements without any kind of extra added stabilization.

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arXiv ID1611.04509 (version 2)
Pith IDEZU5TJ5J, Pith's permanent record of this paper and its review
CitationBosco Garc\'ia-Archilla, Javier de Frutos, Julia Novo. "Error analysis of projection methods for non inf-sup stable mixed finite elements. The Navier-Stokes equations." arXiv:1611.04509 (2016). https://pith.science/paper/EZU5TJ5J
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arXiv listing abstract v2. Results and the main claim are underlined; .

We obtain error bounds for a modified Chorin-Teman (Euler non-incremental) method for non inf-sup stable mixed finite elements applied to the evolutionary Navier-Stokes equations. The analysis of the classical Euler non-incremental method is obtained as a particular case. We prove that the modified Euler non-incremental scheme has an inherent stabilization that allows the use of non inf-sup stable mixed finite elements without any kind of extra added stabilization. We show that it is also true in the case of the classical Chorin-Temam method. The relation of the methods with the so called pressure stabilized Petrov Galerkin method (PSPG) is established. We do not assume non-local compatibility conditions for the solution.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We obtain error bounds for a modified Chorin-Teman (Euler non-incremental) method for non inf-sup stable mixed finite elements applied to the evolutionary Navier-Stokes equations. contribution 0.92 0.95 0.34 asserted 1.00
s1 The analysis of the classical Euler non-incremental method is obtained as a particular case. result 0.62 0.83 0.06 asserted 1.00
s2 We prove that the modified Euler non-incremental scheme has an inherent stabilization that allows the use of non inf-sup stable mixed finite elements without any kind of extra added stabilization. result 0.95 0.93 0.70 asserted 1.00
s3 We show that it is also true in the case of the classical Chorin-Temam method. result 0.92 0.84 0.14 asserted 1.00
s4 The relation of the methods with the so called pressure stabilized Petrov Galerkin method (PSPG) is established. contribution 0.64 0.85 0.07 asserted 1.00
s5 We do not assume non-local compatibility conditions for the solution. method 0.39 0.74 0.05 asserted 0.99

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Original abstract

We obtain error bounds for a modified Chorin-Teman (Euler non-incremental) method for non inf-sup stable mixed finite elements applied to the evolutionary Navier-Stokes equations. The analysis of the classical Euler non-incremental method is obtained as a particular case. We prove that the modified Euler non-incremental scheme has an inherent stabilization that allows the use of non inf-sup stable mixed finite elements without any kind of extra added stabilization. We show that it is also true in the case of the classical Chorin-Temam method. The relation of the methods with the so called pressure stabilized Petrov Galerkin method (PSPG) is established. We do not assume non-local compatibility conditions for the solution.

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