A technique to improve the accuracy of the mini-element approximation to incompressible the Navier- Stokes equations is introduced. Once the mini-element approximation has been computed at a fixed time, the linear part of this approximation is postprocessed by solving a discrete Stokes problem. The bubble functions needed to stabilize the approximation to the Navier-Stokes equations are not used at the postprocessing step. This postprocessing procedure allows us to increase by one unit (up to a logarithmic term) the H1 norm rate of convergence of the velocity and correspondingly the L2 norm of the pressure. An error analysis of the algorithm is performed
Ayuso De Dios, B., de Frutos, J., Novo, J. (2007). Improving the accuracy of the mini-element approximation to Navier-Stokes equations. IMA JOURNAL OF NUMERICAL ANALYSIS, 27(1), 198-218 [10.1093/imanum/drl010].
Improving the accuracy of the mini-element approximation to Navier-Stokes equations
Ayuso De Dios, BP;
2007
Abstract
A technique to improve the accuracy of the mini-element approximation to incompressible the Navier- Stokes equations is introduced. Once the mini-element approximation has been computed at a fixed time, the linear part of this approximation is postprocessed by solving a discrete Stokes problem. The bubble functions needed to stabilize the approximation to the Navier-Stokes equations are not used at the postprocessing step. This postprocessing procedure allows us to increase by one unit (up to a logarithmic term) the H1 norm rate of convergence of the velocity and correspondingly the L2 norm of the pressure. An error analysis of the algorithm is performed
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