A Viscosity-Independent Error Estimate of a Pressure-Stabilized Lagrange–Galerkin Scheme for the Oseen Problem

We consider a pressure-stabilized Lagrange–Galerkin scheme for the transient Oseen problem with small viscosity. In the scheme we use the equal-order approximation of order k for both the velocity and pressure, and add a symmetric pressure stabilization term. We show an error estimate for the veloci...

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Bibliographic Details
Published inJournal of scientific computing Vol. 80; no. 2; pp. 834 - 858
Main Author Uchiumi, Shinya
Format Journal Article
LanguageEnglish
Published New York Springer US 01.08.2019
Springer Nature B.V
Subjects
Algorithms
Approximation
Computational Mathematics and Numerical Analysis
Errors
Exact solutions
Finite element analysis
Galerkin method
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Ordinary differential equations
Theoretical
Velocity
Viscosity
Transient Oseen problem
Finite element method
65M25
65M60
Equal-order elements
76D07
Lagrange–Galerkin scheme
Dependence on viscosity
65M12
76M10
Symmetric pressure stabilization
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Summary:We consider a pressure-stabilized Lagrange–Galerkin scheme for the transient Oseen problem with small viscosity. In the scheme we use the equal-order approximation of order k for both the velocity and pressure, and add a symmetric pressure stabilization term. We show an error estimate for the velocity with a constant independent of the viscosity if the exact solution is sufficiently smooth. We also show an error estimate of a discrete primitive of the pressure. Numerical examples show high accuracy of the scheme for problems with small viscosity.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-019-00958-7