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Analysis of a projection method for the Stokes problem using an ε-Stokes approach
Kanazawa University, Japan.
Kanazawa University, Japan.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).ORCID iD: 0000-0002-1160-0007
Japan Science and Technology Agency, PRESTO, Japan.
2019 (English)In: Japan journal of industrial and applied mathematics, ISSN 0916-7005, E-ISSN 1868-937X, Vol. 36, no 3, p. 959-985Article in journal (Refereed) Published
Abstract [en]

We generalize pressure boundary conditions of an ε-Stokes problem. Our ε-Stokes problem connects the classical Stokes problem and the corresponding pressure-Poisson equation using one parameter ε>0. For the Dirichlet boundary condition, it is proven in Matsui and Muntean (Adv Math Sci Appl, 27:181–191,2018) that the solution for the ε-Stokes problem converges to the one for the Stokes problem as ε tends to 0, and to the one for the pressure-Poisson problem as εtends to ∞. Here, we extend these results to the Neumann and mixed boundary conditions. We also establis herror estimates in suitable norms between the solutions to the ε-Stokes problem, the pressure-Poisson problem and the Stokes problem, respectively. Several numerical examples are provided to show that several such error estimates are optimal in ε. Our error estimates are improved if one uses the Neumann boundary conditions. In addition, we show that the solution to the ε-Stokes problem has a nice asymptotic structure.

Place, publisher, year, edition, pages
Springer, 2019. Vol. 36, no 3, p. 959-985
Keywords [en]
Stokes problem, Pressure-Poisson equation, Asymptotic analysis, Finite element method
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-73443DOI: 10.1007/s13160-019-00373-3ISI: 000487968400012OAI: oai:DiVA.org:kau-73443DiVA, id: diva2:1335376
Funder
The Swedish Foundation for International Cooperation in Research and Higher Education (STINT)Available from: 2019-07-05 Created: 2019-07-05 Last updated: 2019-11-12Bibliographically approved

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Muntean, Adrian

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